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Adaptive Sampling of Pareto Frontiers with Binary Constraints Using Regression and Classification

Raoul Heese, Michael Bortz

Auto-TLDR; Adaptive Optimization for Black-Box Multi-Objective Optimizing Problems with Binary Constraints

Abstract Poster

We present a novel adaptive optimization algorithm for black-box multi-objective optimization problems with binary constraints on the foundation of Bayes optimization. Our method is based on probabilistic regression and classification models, which act as a surrogate for the optimization goals and allow us to suggest multiple design points at once in each iteration. The proposed acquisition function is intuitively understandable and can be tuned to the demands of the problems at hand. We also present a novel ellipsoid truncation method to speed up the expected hypervolume calculation in a straightfoward way for regression models with a normal probability density. We benchmark our approach with an evolutionary algorithm on multiple test problems.

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3CS Algorithm for Efficient Gaussian Process Model Retrieval

Fabian Berns, Kjeld Schmidt, Ingolf Bracht, Christian Beecks

Auto-TLDR; Efficient retrieval of Gaussian Process Models for large-scale data using divide-&-conquer-based approach

Abstract Slides Poster Similar

Gaussian Process Models (GPMs) have been applied for various pattern recognition tasks due to their analytical tractability, ability to quantify uncertainty for their own results as well as to subsume prominent other regression techniques. Despite these promising prospects their super-quadratic computation time complexity for model selection and evaluation impedes its broader application for more than a few thousand data points. Although there have been many proposals towards Gaussian Processes for large-scale data, those only offer a linearly scaling improvement to a cubical scaling problem. In particular, solutions like the Nystrom approximation or sparse matrices are only taking fractions of the given data into account and subsequently lead to inaccurate models. In this paper, we thus propose a divide-&-conquer-based approach, that allows to efficiently retrieve GPMs for large-scale data. The resulting model is composed of independent pattern representations for non-overlapping segments of the given data and consequently reduces computation time significantly. Our performance analysis indicates that our proposal is able to outperform state-of-the-art algorithms for GPM retrieval with respect to the qualities of efficiency and accuracy.

A Multilinear Sampling Algorithm to Estimate Shapley Values

Ramin Okhrati, Aldo Lipani

Auto-TLDR; A sampling method for Shapley values for multilayer Perceptrons

Abstract Slides Poster Similar

Shapley values are great analytical tools in game theory to measure the importance of a player in a game. Due to their axiomatic and desirable properties such as efficiency, they have become popular for feature importance analysis in data science and machine learning. However, the time complexity to compute Shapley values based on the original formula is exponential, and as the number of features increases, this becomes infeasible. Castro et al. [1] developed a sampling algorithm, to estimate Shapley values. In this work, we propose a new sampling method based on a multilinear extension technique as applied in game theory. The aim is to provide a more efficient (sampling) method for estimating Shapley values. Our method is applicable to any machine learning model, in particular for either multiclass classifications or regression problems. We apply the method to estimate Shapley values for multilayer Perceptrons (MLPs) and through experimentation on two datasets, we demonstrate that our method provides more accurate estimations of the Shapley values by reducing the variance of the sampling statistics

Multi-annotator Probabilistic Active Learning

Marek Herde, Daniel Kottke, Denis Huseljic, Bernhard Sick

Auto-TLDR; MaPAL: Multi-annotator Probabilistic Active Learning

Abstract Slides Poster Similar

Classifiers require annotations of instances, i.e., class labels, for training. An annotation process is often costly due to its manual execution through human annotators. Active learning (AL) aims at reducing the annotation costs by selecting instances from which the classifier is expected to learn the most. Many AL strategies assume the availability of a single omniscient annotator. In this article, we overcome this limitation by considering multiple error-prone annotators. We propose a novel AL strategy multi-annotator probabilistic active learning (MaPAL). Due to the nature of learning with error-prone annotators, it must not only select instances but annotators, too. MaPAL builds on a decision-theoretic framework and selects instance-annotator pairs maximizing the classifier's expected performance. Experiments on a variety of data sets demonstrate MaPAL's superior performance compared to five related AL strategies.

Automatically Mining Relevant Variable Interactions Via Sparse Bayesian Learning

Ryoichiro Yafune, Daisuke Sakuma, Yasuo Tabei, Noritaka Saito, Hiroto Saigo

Auto-TLDR; Sparse Bayes for Interpretable Non-linear Prediction

Abstract Slides Poster Similar

With the rapid increase in the availability of large amount of data, prediction is becoming increasingly popular, and has widespread through our daily life. However, powerful non- linear prediction methods such as deep learning and SVM suffer from interpretability problem, making it hard to use in domains where the reason for decision making is required. In this paper, we develop an interpretable non-linear model called itemset Sparse Bayes (iSB), which builds a Bayesian probabilistic model, while simultaneously considering variable interactions. In order to suppress the resulting large number of variables, sparsity is imposed on regression weights by a sparsity inducing prior. As a subroutine to search for variable interactions, itemset enumeration algorithm is employed with a novel bounding condition. In computational experiments using real-world dataset, the proposed method performed better than decision tree by 10% in terms of r-squared . We also demonstrated the advantage of our method in Bayesian optimization setting, in which the proposed approach could successfully find the maximum of an unknown function faster than Gaussian process. The interpretability of iSB is naturally inherited to Bayesian optimization, thereby gives us a clue to understand which variables interactions are important in optimizing an unknown function.

Budgeted Batch Mode Active Learning with Generalized Cost and Utility Functions

Arvind Agarwal, Shashank Mujumdar, Nitin Gupta, Sameep Mehta

Auto-TLDR; Active Learning Based on Utility and Cost Functions

Abstract Slides Poster Similar

Active learning reduces the labeling cost by actively querying labels for the most valuable data points. Typical active learning methods select the most informative examples one-at-a-time, their batch variants exist where a set of most informative points are selected. These points are selected in such a way that when added to the training data along with their labels, they provide maximum benefit to the underlying model. In this paper, we present a learning framework that actively selects optimal set of examples (in a batch) within a given budget, based on given utility and cost functions. The framework is generic enough to incorporate any utility and any cost function defined on a set of examples. Furthermore, we propose a novel utility function based on the Facility Location problem that considers three important characteristics of utility i.e., diversity, density and point utility. We also propose a novel cost function, by formulating the cost computation problem as an optimization problem, the solution to which turns out to be the minimum spanning tree. Thus, our framework provides the optimal batch of points within the given budget based on the cost and utility functions. We evaluate our method on several data sets and show its superior performance over baseline methods.

Uniform and Non-Uniform Sampling Methods for Sub-Linear Time K-Means Clustering

Yuanhang Ren, Ye Du

Auto-TLDR; Sub-linear Time Clustering with Constant Approximation Ratio for K-Means Problem

Abstract Slides Poster Similar

The $k$-means problem is arguably the most well-known clustering problem in machine learning, and lots of approximation algorithms have been proposed for it. However, many of these algorithms may become infeasible when data is huge. Sub-linear time algorithms with constant approximation ratios are desirable in this scenario. In this paper, we first improve the analysis of the algorithm proposed by \cite{Mohan:2017:BNA:3172077.3172235} by sharpening the approximation ratio from $4(\alpha+\beta)$ to $\alpha+\beta$. Moreover, on mild assumptions of the data, a constant approximation ratio can be achieved in poly-logarithmic time by the algorithm. Furthermore, we propose a novel sub-linear time clustering algorithm called {\it Double-K-M$\text{C}^2$ sampling} as well. Experiments on the data clustering task and the image segmentation task have validated the effectiveness of our algorithms.

Active Sampling for Pairwise Comparisons via Approximate Message Passing and Information Gain Maximization

Aliaksei Mikhailiuk, Clifford Wilmot, Maria Perez-Ortiz, Dingcheng Yue, Rafal Mantiuk

Auto-TLDR; ASAP: An Active Sampling Algorithm for Pairwise Comparison Data

Abstract Slides Similar

Pairwise comparison data arise in many domains with subjective assessment experiments, for example in image and video quality assessment. In these experiments observers are asked to express a preference between two conditions. However, many pairwise comparison protocols require a large number of comparisons to infer accurate scores, which may be unfeasible when each comparison is time-consuming (e.g. videos) or expensive (e.g. medical imaging). This motivates the use of an active sampling algorithm that chooses only the most informative pairs for comparison. In this paper we propose ASAP, an active sampling algorithm based on approximate message passing and expected information gain maximization. Unlike most existing methods, which rely on partial updates of the posterior distribution, we are able to perform full updates and therefore much improve the accuracy of the inferred scores. The algorithm relies on three techniques for reducing computational cost: inference based on approximate message passing, selective evaluations of the information gain, and selecting pairs in a batch that forms a minimum spanning tree of the inverse of information gain. We demonstrate, with real and synthetic data, that ASAP offers the highest accuracy of inferred scores compared to the existing methods. We also provide an open-source GPU implementation of ASAP for large-scale experiments.

Learning Sign-Constrained Support Vector Machines

Kenya Tajima, Kouhei Tsuchida, Esmeraldo Ronnie Rey Zara, Naoya Ohta, Tsuyoshi Kato

Auto-TLDR; Constrained Sign Constraints for Learning Linear Support Vector Machine

Abstract Poster Similar

Domain knowledge is useful to improve the generalization performance of learning machines. Sign constraints are a handy representation to combine domain knowledge with learning machine. In this paper, we consider constraining the signs of the weight coefficients in learning the linear support vector machine, and develop two optimization algorithms for minimizing the empirical risk under the sign constraints. One of the two algorithms is based on the projected gradient method, in which each iteration of the projected gradient method takes O(nd) computational cost and the sublinear convergence of the objective error is guaranteed. The second algorithm is based on the Frank-Wolfe method that also converges sublinearly and possesses a clear termination criterion. We show that each iteration of the Frank-Wolfe also requires O(nd) cost. Furthermore, we derive the explicit expression for the minimal iteration number to ensure an epsilon-accurate solution by analyzing the curvature of the objective function. Finally, we empirically demonstrate that the sign constraints are a promising technique when similarities to the training examples compose the feature vector.

Bayesian Active Learning for Maximal Information Gain on Model Parameters

Kasra Arnavaz, Aasa Feragen, Oswin Krause, Marco Loog

Auto-TLDR; Bayesian assumptions for Bayesian classification

Abstract Slides Poster Similar

The fact that machine learning models, despite their advancements, are still trained on randomly gathered data is proof that a lasting solution to the problem of optimal data gathering has not yet been found. In this paper, we investigate whether a Bayesian approach to the classification problem can provide assumptions under which one is guaranteed to perform at least as good as random sampling. For a logistic regression model, we show that maximal expected information gain on model parameters is a promising criterion for selecting samples, assuming that our classification model is well-matched to the data. Our derived criterion is closely related to the maximum model change. We experiment with data sets which satisfy this assumption to varying degrees to see how sensitive our performance is to the violation of our assumption in practice.

Adaptive Matching of Kernel Means

Miao Cheng, Xinge You

Auto-TLDR; Adaptive Matching of Kernel Means for Knowledge Discovery and Feature Learning

Abstract Slides Poster Similar

As a promising step, the performance of data analysis and feature learning are able to be improved if certain pattern matching mechanism is available. One of the feasible solutions can refer to the importance estimation of instances, and consequently, kernel mean matching (KMM) has become an important method for knowledge discovery and novelty detection in general. Furthermore, the existing KMM methods have focused on concrete learning frameworks. In this work, a novel approach to adaptive matching of kernel means is proposed, and selected data with high importance are adopted to achieve calculation efficiency with optimization. In addition, scalable learning can be conducted in proposed method as a generalized solution with appended data. The experimental results on a wide variety of real-world data sets demonstrate the proposed method is able to give outstanding performance compared with several state-of-the-art methods, while calculation efficiency can be preserved.

Watermelon: A Novel Feature Selection Method Based on Bayes Error Rate Estimation and a New Interpretation of Feature Relevance and Redundancy

Xiang Xie, Wilhelm Stork

Auto-TLDR; Feature Selection Using Bayes Error Rate Estimation for Dynamic Feature Selection

Abstract Slides Poster Similar

Feature selection has become a crucial part of many classification problems in which high-dimensional datasets may contain tens of thousands of features. In this paper, we propose a novel feature selection method scoring the features through estimating the Bayes error rate based on kernel density estimation. Additionally, we update the scores of features dynamically by quantitatively interpreting the effects of feature relevance and redundancy in a new way. Distinguishing from the common heuristic applied by many feature selection methods, which prefers choosing features that are not relevant to each other, our approach penalizes only monotonically correlated features and rewards any other kind of relevance among features based on Spearman’s rank correlation coefficient and normalized mutual information. We conduct extensive experiments on seventeen diverse classification benchmarks, the results show that our approach overperforms other seventeen popular state-of-the-art feature selection methods in most cases.

Factor Screening Using Bayesian Active Learning and Gaussian Process Meta-Modelling

Cheng Li, Santu Rana, Andrew William Gill, Dang Nguyen, Sunil Kumar Gupta, Svetha Venkatesh

Auto-TLDR; Data-Efficient Bayesian Active Learning for Factor Screening in Combat Simulations

Abstract Similar

In this paper we propose a data-efficient Bayesian active learning framework for factor screening, which is important when dealing with systems which are expensive to evaluate, such as combat simulations. We use Gaussian Process meta-modelling with the Automatic Relevance Determination covariance kernel, which measures the importance of each factor by the inverse of their associated length-scales in the kernel. This importance measures the degree of non-linearity in the simulation response with respect to the corresponding factor. We initially place a prior over the length-scale values, then use the estimated posterior to select the next datum to simulate which maximises the mutual entropy between the length-scales and the unknown simulation response. Our goal-driven Bayesian active learning strategy ensures that we are data-efficient in discovering the correct values of the length-scales compared to either a random-sampling or uncertainty-sampling based approach. We apply our method to an expensive combat simulation and demonstrate the superiority of our approach.

ILS-SUMM: Iterated Local Search for Unsupervised Video Summarization

Yair Shemer, Daniel Rotman, Nahum Shimkin

Auto-TLDR; ILS-SUMM: Iterated Local Search for Video Summarization

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In recent years, there has been an increasing interest in building video summarization tools, where the goal is to automatically create a short summary of an input video that properly represents the original content. We consider shot-based video summarization where the summary consists of a subset of the video shots which can be of various lengths. A straightforward approach to maximize the representativeness of a subset of shots is by minimizing the total distance between shots and their nearest selected shots. We formulate the task of video summarization as an optimization problem with a knapsack-like constraint on the total summary duration. Previous studies have proposed greedy algorithms to solve this problem approximately, but no experiments were presented to measure the ability of these methods to obtain solutions with low total distance. Indeed, our experiments on video summarization datasets show that the success of current methods in obtaining results with low total distance still has much room for improvement. In this paper, we develop ILS-SUMM, a novel video summarization algorithm to solve the subset selection problem under the knapsack constraint. Our algorithm is based on the well-known metaheuristic optimization framework -- Iterated Local Search (ILS), known for its ability to avoid weak local minima and obtain a good near-global minimum. Extensive experiments show that our method finds solutions with significantly better total distance than previous methods. Moreover, to indicate the high scalability of ILS-SUMM, we introduce a new dataset consisting of videos of various lengths.

The eXPose Approach to Crosslier Detection

Antonio Barata, Frank Takes, Hendrik Van Den Herik, Cor Veenman

Auto-TLDR; EXPose: Crosslier Detection Based on Supervised Category Modeling

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Transit of wasteful materials within the European Union is highly regulated through a system of permits. Waste processing costs vary greatly depending on the waste category of a permit. Therefore, companies may have a financial incentive to allege transporting waste with erroneous categorisation. Our goal is to assist inspectors in selecting potentially manipulated permits for further investigation, making their task more effective and efficient. Due to data limitations, a supervised learning approach based on historical cases is not possible. Standard unsupervised approaches, such as outlier detection and data quality-assurance techniques, are not suited since we are interested in targeting non-random modifications in both category and category-correlated features. For this purpose we (1) introduce the concept of crosslier: an anomalous instance of a category which lies across other categories; (2) propose eXPose: a novel approach to crosslier detection based on supervised category modelling; and (3) present the crosslier diagram: a visualisation tool specifically designed for domain experts to easily assess crossliers. We compare eXPose against traditional outlier detection methods in various benchmark datasets with synthetic crossliers and show the superior performance of our method in targeting these instances.

Naturally Constrained Online Expectation Maximization

Daniela Pamplona, Antoine Manzanera

Auto-TLDR; Constrained Online Expectation-Maximization for Probabilistic Principal Components Analysis

Abstract Slides Poster Similar

With the rise of big data sets, learning algorithms must be adapted to piece-wise mechanisms in order to tackle time and memory costs of large scale calculations. Furthermore, for most learning embedded systems the input data are fed in a sequential and contingent manner: one by one, and possibly class by class. Thus, learning algorithms should not only run online but cope with time-varying, non-independent, and non-balanced training data for the system's entire life. Online Expectation-Maximization is a well-known algorithm for learning probabilistic models in real-time, due to its simplicity and convergence properties. However, these properties are only valid in the case of large, independent and identically distributed (iid) samples. In this paper, we propose to constraint the online Expectation-Maximization on the Fisher distance between the parameters. After the presentation of the algorithm, we make a thorough study of its use in Probabilistic Principal Components Analysis. First, we derive the update rules, then we analyse the effect of the constraint on major problems of online and sequential learning: convergence, forgetting and interference. Furthermore we use several algorithmic protocols: iid {\em vs} sequential data, and constraint parameters updated step-wise {\em vs} class-wise. Our results show that this constraint increases the convergence rate of online Expectation-Maximization, decreases forgetting and slightly introduces transfer learning.

Auto Encoding Explanatory Examples with Stochastic Paths

Cesar Ali Ojeda Marin, Ramses J. Sanchez, Kostadin Cvejoski, Bogdan Georgiev

Auto-TLDR; Semantic Stochastic Path: Explaining a Classifier's Decision Making Process using latent codes

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In this paper we ask for the main factors that determine a classifier's decision making process and uncover such factors by studying latent codes produced by auto-encoding frameworks. To deliver an explanation of a classifier's behaviour, we propose a method that provides series of examples highlighting semantic differences between the classifier's decisions. These examples are generated through interpolations in latent space. We introduce and formalize the notion of a semantic stochastic path, as a suitable stochastic process defined in feature (data) space via latent code interpolations. We then introduce the concept of semantic Lagrangians as a way to incorporate the desired classifier's behaviour and find that the solution of the associated variational problem allows for highlighting differences in the classifier decision. Very importantly, within our framework the classifier is used as a black-box, and only its evaluation is required.

Low-Cost Lipschitz-Independent Adaptive Importance Sampling of Stochastic Gradients

Huikang Liu, Xiaolu Wang, Jiajin Li, Man-Cho Anthony So

Auto-TLDR; Adaptive Importance Sampling for Stochastic Gradient Descent

Abstract Slides Similar

Stochastic gradient descent (SGD) usually samples training data based on the uniform distribution, which may not be a good choice because of the high variance of its stochastic gradient. Thus, importance sampling methods are considered in the literature to improve the performance. Most previous work on SGD-based methods with importance sampling requires the knowledge of Lipschitz constants of all component gradients, which are in general difficult to estimate. In this paper, we study an adaptive importance sampling method for common SGD-based methods by exploiting the local first-order information without knowing any Lipschitz constants. In particular, we periodically changes the sampling distribution by only utilizing the gradient norms in the past few iterations. We prove that our adaptive importance sampling non-asymptotically reduces the variance of the stochastic gradients in SGD, and thus better convergence bounds than that for vanilla SGD can be obtained. We extend this sampling method to several other widely used stochastic gradient algorithms including SGD with momentum and ADAM. Experiments on common convex learning problems and deep neural networks illustrate notably enhanced performance using the adaptive sampling strategy.

RNN Training along Locally Optimal Trajectories via Frank-Wolfe Algorithm

Yun Yue, Ming Li, Venkatesh Saligrama, Ziming Zhang

Auto-TLDR; Frank-Wolfe Algorithm for Efficient Training of RNNs

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We propose a novel and efficient training method for RNNs by iteratively seeking a local minima on the loss surface within a small region, and leverage this directional vector for the update, in an outer-loop. We propose to utilize the Frank-Wolfe (FW) algorithm in this context. Although, FW implicitly involves normalized gradients, which can lead to a slow convergence rate, we develop a novel RNN training method that, surprisingly, even with the additional cost, the overall training cost is empirically observed to be lower than back-propagation. Our method leads to a new Frank-Wolfe method, that is in essence an SGD algorithm with a restart scheme. We prove that under certain conditions our algorithm has a sublinear convergence rate of $O(1/\epsilon)$ for $\epsilon$ error. We then conduct empirical experiments on several benchmark datasets including those that exhibit long-term dependencies, and show significant performance improvement. We also experiment with deep RNN architectures and show efficient training performance. Finally, we demonstrate that our training method is robust to noisy data.

Separation of Aleatoric and Epistemic Uncertainty in Deterministic Deep Neural Networks

Denis Huseljic, Bernhard Sick, Marek Herde, Daniel Kottke

Auto-TLDR; AE-DNN: Modeling Uncertainty in Deep Neural Networks

Abstract Slides Poster Similar

Despite the success of deep neural networks (DNN) in many applications, their ability to model uncertainty is still significantly limited. For example, in safety-critical applications such as autonomous driving, it is crucial to obtain a prediction that reflects different types of uncertainty to address life-threatening situations appropriately. In such cases, it is essential to be aware of the risk (i.e., aleatoric uncertainty) and the reliability (i.e., epistemic uncertainty) that comes with a prediction. We present AE-DNN, a model allowing the separation of aleatoric and epistemic uncertainty while maintaining a proper generalization capability. AE-DNN is based on deterministic DNN, which can determine the respective uncertainty measures in a single forward pass. In analyses with synthetic and image data, we show that our method improves the modeling of epistemic uncertainty while providing an intuitively understandable separation of risk and reliability.

Deep Transformation Models: Tackling Complex Regression Problems with Neural Network Based Transformation Models

Beate Sick, Torsten Hothorn, Oliver Dürr

Auto-TLDR; A Deep Transformation Model for Probabilistic Regression

Abstract Slides Poster Similar

We present a deep transformation model for probabilistic regression. Deep learning is known for outstandingly accurate predictions on complex data but in regression tasks it is predominantly used to just predict a single number. This ignores the non-deterministic character of most tasks. Especially if crucial decisions are based on the predictions, like in medical applications, it is essential to quantify the prediction uncertainty. The presented deep learning transformation model estimates the whole conditional probability distribution, which is the most thorough way to capture uncertainty about the outcome. We combine ideas from a statistical transformation model (most likely transformation) with recent transformation models from deep learning (normalizing flows) to predict complex outcome distributions. The core of the method is a parameterized transformation function which can be trained with the usual maximum likelihood framework using gradient descent. The method can be combined with existing deep learning architectures. For small machine learning benchmark datasets, we report state of the art performance for most dataset and partly even outperform it. Our method works for complex input data, which we demonstrate by employing a CNN architecture on image data.

An Invariance-Guided Stability Criterion for Time Series Clustering Validation

Florent Forest, Alex Mourer, Mustapha Lebbah, Hanane Azzag, Jérôme Lacaille

Auto-TLDR; An invariance-guided method for clustering model selection in time series data

Abstract Slides Poster Similar

Time series clustering is a challenging task due to the specificities of this type of data. Temporal correlation and invariance to transformations such as shifting, warping or noise prevent the use of standard data mining methods. Time series clustering has been mostly studied under the angle of finding efficient algorithms and distance metrics adapted to the specific nature of time series data. Much less attention has been devoted to the general problem of model selection. Clustering stability has emerged as a universal and model-agnostic principle for clustering model selection. This principle can be stated as follows: an algorithm should find a structure in the data that is resilient to perturbation by sampling or noise. We propose to apply stability analysis to time series by leveraging prior knowledge on the nature and invariances of the data. These invariances determine the perturbation process used to assess stability. Based on a recently introduced criterion combining between-cluster and within-cluster stability, we propose an invariance-guided method for model selection, applicable to a wide range of clustering algorithms. Experiments conducted on artificial and benchmark data sets demonstrate the ability of our criterion to discover structure and select the correct number of clusters, whenever data invariances are known beforehand.

Camera Calibration Using Parallel Line Segments

Gaku Nakano

Auto-TLDR; Closed-Form Calibration of Surveillance Cameras using Parallel 3D Line Segment Projections

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This paper proposes a camera calibration method suitable for surveillance cameras using the image projection of parallel 3D line segments of the same length. We assume that vertical line segments are perpendicular to the ground plane and their bottom end-points are on the ground plane. Under this assumption, the camera parameters can be directly solved by at least two line segments without estimating vanishing points. Extending the minimal solution, we derive a closed-form solution to the least squares case with more than two line segments. Lens distortion is jointly optimized in bundle adjustment. Synthetic data evaluation shows that the best depression angle of a camera is around 50 degrees. In real data evaluation, we use body joints of pedestrians as vertical line segments. The experimental results on publicly available datasets show that the proposed method with a human pose detector can correctly calibrate wide-angle cameras including radial distortion.

Quantifying Model Uncertainty in Inverse Problems Via Bayesian Deep Gradient Descent

Riccardo Barbano, Chen Zhang, Simon Arridge, Bangti Jin

Auto-TLDR; Bayesian Neural Networks for Inverse Reconstruction via Bayesian Knowledge-Aided Computation

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Recent advances in reconstruction methods for inverse problems leverage powerful data-driven models, e.g., deep neural networks. These techniques have demonstrated state-of-the-art performances for several imaging tasks, but they often do not provide uncertainty on the obtained reconstructions. In this work, we develop a novel scalable data-driven knowledge-aided computational framework to quantify the model uncertainty via Bayesian neural networks. The approach builds on and extends deep gradient descent, a recently developed greedy iterative training scheme, and recasts it within a probabilistic framework. Scalability is achieved by being hybrid in the architecture: only the last layer of each block is Bayesian, while the others remain deterministic, and by being greedy in training. The framework is showcased on one representative medical imaging modality, viz. computed tomography with either sparse view or limited view data, and exhibits competitive performance with respect to state-of-the-art benchmarks, e.g., total variation, deep gradient descent and learned primal-dual.

Stochastic Runge-Kutta Methods and Adaptive SGD-G2 Stochastic Gradient Descent

Gabriel Turinici, Imen Ayadi

Auto-TLDR; Adaptive Stochastic Runge Kutta for the Minimization of the Loss Function

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The minimization of the loss function is of paramount importance in deep neural networks. Many popular optimization algorithms have been shown to correspond to some evolution equation of gradient flow type. Inspired by the numerical schemes used for general evolution equations, we introduce a second-order stochastic Runge Kutta method and show that it yields a consistent procedure for the minimization of the loss function. In addition, it can be coupled, in an adaptive framework, with the Stochastic Gradient Descent (SGD) to adjust automatically the learning rate of the SGD The resulting adaptive SGD, called SGD-G2, shows good results in terms of convergence speed when tested on standard data-sets.

Expectation-Maximization for Scheduling Problems in Satellite Communication

Werner Bailer, Martin Winter, Johannes Ebert, Joel Flavio, Karin Plimon

Auto-TLDR; Unsupervised Machine Learning for Satellite Communication Using Expectation-Maximization

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In this paper we address unsupervised machine learning for two use cases in satellite communication, which are scheduling problems: (i) Ka-band frequency plan optimization and (ii) dynamic configuration of an active antenna array satellite. We apply approaches based on the Expectation-Maximization (EM) framework to both of them. We compare against baselines of currently deployed solutions, and show that they can be significantly outperformed by the EM-based approach. In addition, the approaches can be applied incrementally, thus supporting fast adaptation to small changes in the input configuration.

Aggregating Dependent Gaussian Experts in Local Approximation

Hamed Jalali, Gjergji Kasneci

Auto-TLDR; A novel approach for aggregating the Gaussian experts by detecting strong violations of conditional independence

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Distributed Gaussian processes (DGPs) are prominent local approximation methods to scale Gaussian processes (GPs) to large datasets. Instead of a global estimation, they train local experts by dividing the training set into subsets, thus reducing the time complexity. This strategy is based on the conditional independence assumption, which basically means that there is a perfect diversity between the local experts. In practice, however, this assumption is often violated, and the aggregation of experts leads to sub-optimal and inconsistent solutions. In this paper, we propose a novel approach for aggregating the Gaussian experts by detecting strong violations of conditional independence. The dependency between experts is determined by using a Gaussian graphical model, which yields the precision matrix. The precision matrix encodes conditional dependencies between experts and is used to detect strongly dependent experts and construct an improved aggregation. Using both synthetic and real datasets, our experimental evaluations illustrate that our new method outperforms other state-of-the-art (SOTA) DGP approaches while being substantially more time-efficient than SOTA approaches, which build on independent experts.

Killing Four Birds with One Gaussian Process: The Relation between Different Test-Time Attacks

Kathrin Grosse, Michael Thomas Smith, Michael Backes

Auto-TLDR; Security of Gaussian Process Classifiers against Attack Algorithms

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In machine learning (ML) security, attacks like evasion, model stealing or membership inference are generally studied in individually. Previous work has also shown a relationship between some attacks and decision function curvature of the targeted model. Consequently, we study an ML model allowing direct control over the decision surface curvature: Gaussian Process classifiers (GPCs). For evasion, we find that changing GPC's curvature to be robust against one attack algorithm boils down to enabling a different norm or attack algorithm to succeed. This is backed up by our formal analysis showing that static security guarantees are opposed to learning. Concerning intellectual property, we show formally that lazy learning does not necessarily leak all information when applied. In practice, often a seemingly secure curvature can be found. For example, we are able to secure GPC against empirical membership inference by proper configuration. In this configuration, however, the GPC's hyper-parameters are leaked, e.g. model reverse engineering succeeds. We conclude that attacks on classification should not be studied in isolation, but in relation to each other.

Probabilistic Word Embeddings in Kinematic Space

Adarsh Jamadandi, Rishabh Tigadoli, Ramesh Ashok Tabib, Uma Mudenagudi

Auto-TLDR; Kinematic Space for Hierarchical Representation Learning

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In this paper, we propose a method for learning representations in the space of Gaussian-like distribution defined on a novel geometrical space called Kinematic space. The utility of non-Euclidean geometry for deep representation learning has gained traction, specifically different models of hyperbolic geometry such as Poincar\'{e} and Lorentz models have proven useful for learning hierarchical representations. Going beyond manifolds with constant curvature, albeit has better representation capacity might lead to unhanding of computationally tractable tools like Riemannian optimization methods. Here, we explore a pseudo-Riemannian auxiliary Lorentzian space called Kinematic space and provide a principled approach for constructing a Gaussian-like distribution, which is compatible with gradient-based learning methods, to formulate a probabilistic word embedding framework. Contrary to, mapping lexically distributed representations to a single point vector in Euclidean space, we advocate for mapping entities to density-based representations, as it provides explicit control over the uncertainty in representations. We test our framework by embedding WordNet-Noun hierarchy, a large lexical database, our experiments report strong consistent improvements in Mean Rank and Mean Average Precision (MAP) values compared to probabilistic word embedding frameworks defined on Euclidean and hyperbolic spaces. Our framework reports a significant 83.140\% improvement in Mean Rank compared to Euclidean version and an improvement of 79.416\% over hyperbolic version. Our work serves as an evidence for the utility of novel geometrical spaces for learning hierarchical representations.

Mean Decision Rules Method with Smart Sampling for Fast Large-Scale Binary SVM Classification

Alexandra Makarova, Mikhail Kurbakov, Valentina Sulimova

Auto-TLDR; Improving Mean Decision Rule for Large-Scale Binary SVM Problems

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This paper relies on the Mean Decision Rule (MDR) method for solving large-scale binary SVM problems. It consists in taking small random samples of the full dataset and separate training for each of them with consecutive averaging the respective individual decision rules to obtain a final one. This paper proposes two new approaches to improve it. The first proposed approach is a new sampling technique that exploits SVM and MDR properties to fast form so called smart samples by selecting only the objects, that are candidates to be the support ones. The proposed technique essentially increases MDR convergence and allows to reach the highest quality in less time. In the case of kernel-based MDR (KMDR) the proposed sampling technique allows additionally to reduce the number of support objects in the final decision rule and, as a result, to decrease the recognition time. The second proposed approach is a new data strategy to accelerate random access to large datasets stored in the traditional libsvm format. The proposed strategy allows to quickly extract random subsets of objects from a file and load them into RAM, and is it also suitable for any sampling-based methods, including stochastic gradient methods. Joint using of the proposed approaches with (K)MDR allows to obtain the best (or near the best) decision of large-scale binary SVM problems faster, compared to the existing SVM solvers.

GPSRL: Learning Semi-Parametric Bayesian Survival Rule Lists from Heterogeneous Patient Data

Ameer Hamza Shakur, Xiaoning Qian, Zhangyang Wang, Bobak Mortazavi, Shuai Huang

Auto-TLDR; Semi-parametric Bayesian Survival Rule List Model for Heterogeneous Survival Data

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Survival data is often collected in medical applications from a heterogeneous population of patients. While in the past, popular survival models focused on modeling the average effect of the co-variates on survival outcomes, rapidly advancing sensing and information technologies have provided opportunities to further model the heterogeneity of the population as well as the non-linearity of the survival risk. With this motivation, we propose a new semi-parametric Bayesian Survival Rule List model in this paper. Our model derives a rule-based decision-making approach, while within the regime defined by each rule, survival risk is modelled via a Gaussian process latent variable model. Markov Chain Monte Carlo with a nested Laplace approximation for the latent variable model is used to search over the posterior of the rule lists efficiently. The use of ordered rule lists enables us to model heterogeneity while keeping the model complexity in check. Performance evaluations on a synthetic heterogeneous survival dataset and a real world sepsis survival dataset demonstrate the effectiveness of our model.

Sketch-Based Community Detection Via Representative Node Sampling

Mahlagha Sedghi, Andre Beckus, George Atia

Auto-TLDR; Sketch-based Clustering of Community Detection Using a Small Sketch

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This paper proposes a sketch-based approach to the community detection problem which clusters the full graph through the use of an informative and concise sketch. The reduced sketch is built through an effective sampling approach which selects few nodes that best represent the complete graph and operates on a pairwise node similarity measure based on the average commute time. After sampling, the proposed algorithm clusters the nodes in the sketch, and then infers the cluster membership of the remaining nodes in the full graph based on their aggregate similarity to nodes in the partitioned sketch. By sampling nodes with strong representation power, our approach can improve the success rates over full graph clustering. In challenging cases with large node degree variation, our approach not only maintains competitive accuracy with full graph clustering despite using a small sketch, but also outperforms existing sampling methods. The use of a small sketch allows considerable storage savings, and computational and timing improvements for further analysis such as clustering and visualization. We provide numerical results on synthetic data based on the homogeneous, heterogeneous and degree corrected versions of the stochastic block model, as well as experimental results on real-world data.

Relative Feature Importance

Gunnar König, Christoph Molnar, Bernd Bischl, Moritz Grosse-Wentrup

Auto-TLDR; Relative Feature Importance for Interpretable Machine Learning

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Interpretable Machine Learning (IML) methods are used to gain insight into the relevance of a feature of interest for the performance of a model. Commonly used IML methods differ in whether they consider features of interest in isolation, e.g., Permutation Feature Importance (PFI), or in relation to all remaining feature variables, e.g., Conditional Feature Importance (CFI). As such, the perturbation mechanisms inherent to PFI and CFI represent extreme reference points. We introduce Relative Feature Importance (RFI), a generalization of PFI and CFI that allows for a more nuanced feature importance computation beyond the PFI versus CFI dichotomy. With RFI, the importance of a feature relative to any other subset of features can be assessed, including variables that were not available at training time. We derive general interpretation rules for RFI based on a detailed theoretical analysis of the implications of relative feature relevance, and demonstrate the method's usefulness on simulated examples.

Creating Classifier Ensembles through Meta-Heuristic Algorithms for Aerial Scene Classification

Álvaro Roberto Ferreira Jr., Gustavo Gustavo Henrique De Rosa, Joao Paulo Papa, Gustavo Carneiro, Fabio Augusto Faria

Auto-TLDR; Univariate Marginal Distribution Algorithm for Aerial Scene Classification Using Meta-Heuristic Optimization

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Aerial scene classification is a challenging task to be solved in the remote sensing area, whereas deep learning approaches, such as Convolutional Neural Networks (CNN), are being widely employed to overcome such a problem. Nevertheless, it is not straightforward to find single CNN models that can solve all aerial scene classification tasks, allowing the nurturing of a better alternative, which is to fuse CNN-based classifiers into an ensemble. However, an appropriate choice of the classifiers that will belong to the ensemble is a critical factor, as it is unfeasible to employ all the possible classifiers in the literature. Therefore, this work proposes a novel framework based on meta-heuristic optimization for creating optimized-ensembles in the context of aerial scene classification. The experimental results were performed across nine meta-heuristic algorithms and three aerial scene literature datasets, being compared in terms of effectiveness (accuracy), efficiency (execution time), and behavioral performance in different scenarios. Finally, one can observe that the Univariate Marginal Distribution Algorithm (UMDA) overcame popular literature meta-heuristic algorithms, such as Genetic Programming and Particle Swarm Optimization considering the adopted criteria in the performed experiments.

Understanding Integrated Gradients with SmoothTaylor for Deep Neural Network Attribution

Gary Shing Wee Goh, Sebastian Lapuschkin, Leander Weber, Wojciech Samek, Alexander Binder

Auto-TLDR; SmoothGrad: bridging Integrated Gradients and SmoothGrad from the Taylor's theorem perspective

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Integrated Gradients as an attribution method for deep neural network models offers simple implementability. However, it suffers from noisiness of explanations which affects the ease of interpretability. The SmoothGrad technique is proposed to solve the noisiness issue and smoothen the attribution maps of any gradient-based attribution method. In this paper, we present SmoothTaylor as a novel theoretical concept bridging Integrated Gradients and SmoothGrad, from the Taylor's theorem perspective. We apply the methods to the image classification problem, using the ILSVRC2012 ImageNet object recognition dataset, and a couple of pretrained image models to generate attribution maps. These attribution maps are empirically evaluated using quantitative measures for sensitivity and noise level. We further propose adaptive noising to optimize for the noise scale hyperparameter value. From our experiments, we find that the SmoothTaylor approach together with adaptive noising is able to generate better quality saliency maps with lesser noise and higher sensitivity to the relevant points in the input space as compared to Integrated Gradients.

Deep Learning on Active Sonar Data Using Bayesian Optimization for Hyperparameter Tuning

Henrik Berg, Karl Thomas Hjelmervik

Auto-TLDR; Bayesian Optimization for Sonar Operations in Littoral Environments

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Sonar operations in littoral environments may be challenging due to an increased probability of false alarms. Machine learning can be used to train classifiers that are able to filter out most of the false alarms automatically, however, this is a time consuming process, with many hyperparameters that need to be tuned in order to yield useful results. In this paper, Bayesian optimization is used to search for good values for some of the hyperparameters, like topology and training parameters, resulting in performance superior to earlier trial-and-error based training. Additionally, we analyze some of the parameters involved in the Bayesian optimization, as well as the resulting hyperparameter values.

Wasserstein k-Means with Sparse Simplex Projection

Takumi Fukunaga, Hiroyuki Kasai

Auto-TLDR; SSPW $k$-means: Sparse Simplex Projection-based Wasserstein $ k$-Means Algorithm

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This paper presents a proposal of a faster Wasserstein $k$-means algorithm for histogram data by reducing Wasserstein distance computations exploiting sparse simplex projection. We shrink data samples, centroids and ground cost matrix, which enables significant reduction of the computations to solve optimal transport problems without loss of clustering quality. Furthermore, we dynamically reduce computational complexity by removing lower-valued data samples harnessing sparse simplex projection while keeping degradation of clustering quality lower. We designate this proposed algorithm as sparse simplex projection-based Wasserstein $k$-means, for short, SSPW $k$-means. Numerical evaluations against Wasserstein $k$-means algorithm demonstrate the effectiveness of the proposed SSPW $k$-means on real-world datasets.

Exact and Convergent Iterative Methods to Compute the Orthogonal Point-To-Ellipse Distance

Siyu Guo, Pingping Hu, Zhigang Ling, He Wen, Min Liu, Lu Tang

Auto-TLDR; Convergent iterative algorithm for orthogonal distance based ellipse fitting

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Computation of the orthogonal distance from a given point to an ellipse is the basis of orthogonal distance based ellipse fitting methods. The problem of this orthogonal distance and the corresponding orthogonal contacting point on the ellipse is investigated, and two algorithms, the exact one and the convergent iterative one, are proposed. The exact algorithm utilizes the closed form solution of quartic equations, but is numerically unstable. The iterative algorithm, however, uses Newton’s method to solve the equation, and starts from an initial solution that is proven to lead to a convergent iteration. The proposed algorithms are compared in experiments with an existing rival. Although the rival algorithm is slightly faster and more accurate in realistic scenarios, divergence is likely to occur. On the other hand, both our exact and iterative algorithms can reliably produce the solution needed. While the exact algorithm encounters numeric instability, the iterative algorithm is only slightly outperformed by the existing rival in speed and accuracy, but at the same time provides more reliable computation process, thus making it a preferable method for the task.

On Resource-Efficient Bayesian Network Classifiers and Deep Neural Networks

Wolfgang Roth, Günther Schindler, Holger Fröning, Franz Pernkopf

Auto-TLDR; Quantization-Aware Bayesian Network Classifiers for Small-Scale Scenarios

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We present two methods to reduce the complexity of Bayesian network (BN) classifiers. First, we introduce quantization-aware training using the straight-through gradient estimator to quantize the parameters of BNs to few bits. Second, we extend a recently proposed differentiable tree-augmented naive Bayes (TAN) structure learning approach to also consider the model size. Both methods are motivated by recent developments in the deep learning community, and they provide effective means to trade off between model size and prediction accuracy, which is demonstrated in extensive experiments. Furthermore, we contrast quantized BN classifiers with quantized deep neural networks (DNNs) for small-scale scenarios which have hardly been investigated in the literature. We show Pareto optimal models with respect to model size, number of operations, and test error and find that both model classes are viable options.

Temporal Pattern Detection in Time-Varying Graphical Models

Federico Tomasi, Veronica Tozzo, Annalisa Barla

Auto-TLDR; A dynamical network inference model that leverages on kernels to consider general temporal patterns

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Graphical models allow to describe the interplay among variables of a system through a compact representation, suitable when relations evolve over time. For example, in a biological setting, genes interact differently depending on external environmental or metabolic factors. To incorporate this dynamics a viable strategy is to estimate a sequence of temporally related graphs assuming similarity among samples in different time points. While adjacent time points may direct the analysis towards a robust estimate of the underlying graph, the resulting model will not incorporate long-term or recurrent temporal relationships. In this work we propose a dynamical network inference model that leverages on kernels to consider general temporal patterns (such as circadian rhythms or seasonality). We show how our approach may also be exploited when the recurrent patterns are unknown, by coupling the network inference with a clustering procedure that detects possibly non-consecutive similar networks. Such clusters are then used to build similarity kernels. The convexity of the functional is determined by whether we impose or infer the kernel. In the first case, the optimisation algorithm exploits efficiently proximity operators with closed-form solutions. In the other case, we resort to an alternating minimisation procedure which jointly learns the temporal kernel and the underlying network. Extensive analysis on synthetic data shows the efficacy of our models compared to state-of-the-art methods. Finally, we applied our approach on two real-world applications to show how considering long-term patterns is fundamental to have insights on the behaviour of a complex system.

Switching Dynamical Systems with Deep Neural Networks

Cesar Ali Ojeda Marin, Kostadin Cvejoski, Bogdan Georgiev, Ramses J. Sanchez

Auto-TLDR; Variational RNN for Switching Dynamics

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The problem of uncovering different dynamicalregimes is of pivotal importance in time series analysis. Switchingdynamical systems provide a solution for modeling physical phe-nomena whose time series data exhibit different dynamical modes.In this work we propose a novel variational RNN model forswitching dynamics allowing for both non-Markovian and non-linear dynamical behavior between and within dynamic modes.Attention mechanisms are provided to inform the switchingdistribution. We evaluate our model on synthetic and empiricaldatasets of diverse nature and successfully uncover differentdynamical regimes and predict the switching dynamics.

Fast Approximate Modelling of the Next Combination Result for Stopping the Text Recognition in a Video

Konstantin Bulatov, Nadezhda Fedotova, Vladimir V. Arlazarov

Auto-TLDR; Stopping Video Stream Recognition of a Text Field Using Optimized Computation Scheme

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In this paper, we consider a task of stopping the video stream recognition process of a text field, in which each frame is recognized independently and the individual results are combined together. The video stream recognition stopping problem is an under-researched topic with regards to computer vision, but its relevance for building high-performance video recognition systems is clear. Firstly, we describe an existing method of optimally stopping such a process based on a modelling of the next combined result. Then, we describe approximations and assumptions which allowed us to build an optimized computation scheme and thus obtain a method with reduced computational complexity. The methods were evaluated for the tasks of document text field recognition and arbitrary text recognition in a video. The experimental comparison shows that the introduced approximations do not diminish the quality of the stopping method in terms of the achieved combined result precision, while dramatically reducing the time required to make the stopping decision. The results were consistent for both text recognition tasks.

Towards Explaining Adversarial Examples Phenomenon in Artificial Neural Networks

Ramin Barati, Reza Safabakhsh, Mohammad Rahmati

Auto-TLDR; Convolutional Neural Networks and Adversarial Training from the Perspective of convergence

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In this paper, we study the adversarial examples existence and adversarial training from the standpoint of convergence and provide evidence that pointwise convergence in ANNs can explain these observations. The main contribution of our proposal is that it relates the objective of the evasion attacks and adversarial training with concepts already defined in learning theory. Also, we extend and unify some of the other proposals in the literature and provide alternative explanations on the observations made in those proposals. Through different experiments, we demonstrate that the framework is valuable in the study of the phenomenon and is applicable to real-world problems.

Kernel-Based LIME with Feature Dependency Sampling

Sheng Shi, Yangzhou Du, Fan Wei

Auto-TLDR; Local Interpretable Model-agnostic Explanation with Feature Dependency Sampling

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While deep learning makes significant achievements in Artificial Intelligence (AI), the lack of transparency has limited its broad application in various vertical domains. Explainability is not only a gateway between AI and society, but also a powerful feature to detect flaw of the models and bias of the data. Local Interpretable Model-agnostic Explanation (LIME) is a widely-accepted technique that explains the predictions of any classifier faithfully by learning an interpretable model locally around the predicted instance. However, the sampling operation in the standard implementation of LIME is defective. Perturbed samples are generated from a uniform distribution, ignoring the complicated correlation between features. Moreover, as the local decision boundary is non-linear for most complex networks, linear approximation may produce serious errors. This paper proposes an high-interpretability and high-fidelity local explanation method, known as Kernel-based LIME with Feature Dependency Sampling (KLFDS). Given an instance being explained, KLFDS enhances interpretability by feature sampling with intrinsic dependency. Besides, KLFDS improves the local explanation fidelity by approximating nonlinear boundary of local decision. We evaluate our method with image classification tasks and results show that KLFDS's explanation of the back-box model achieves much better performance than original LIME in terms of interpretability and fidelity.

Label Self-Adaption Hashing for Image Retrieval

Jianglin Lu, Zhihui Lai, Hailing Wang, Jie Zhou

Auto-TLDR; Label Self-Adaption Hashing for Large-Scale Image Retrieval

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Hashing has attracted widespread attention in image retrieval because of its fast retrieval speed and low storage cost. Compared with supervised methods, unsupervised hashing methods are more reasonable and suitable for large-scale image retrieval since it is always difficult and expensive to collect true labels of the massive data. Without label information, however, unsupervised hashing methods can not guarantee the quality of learned binary codes. To resolve this dilemma, this paper proposes a novel unsupervised hashing method called Label Self-Adaption Hashing (LSAH), which contains effective hashing function learning part and self-adaption label generation part. In the first part, we utilize anchor graph to keep the local structure of the data and introduce joint sparsity into the model to extract effective features for high-quality binary code learning. In the second part, a self-adaptive cluster label matrix is learned from the data under the assumption that the nearest neighbor points should have a large probability to be in the same cluster. Therefore, the proposed LSAH can make full use of the potential discriminative information of the data to guide the learning of binary code. It is worth noting that LSAH can learn effective binary codes, hashing function and cluster labels simultaneously in a unified optimization framework. To solve the resulting optimization problem, an Augmented Lagrange Multiplier based iterative algorithm is elaborately designed. Extensive experiments on three large-scale data sets indicate the promising performance of the proposed LSAH.

Feature Extraction by Joint Robust Discriminant Analysis and Inter-Class Sparsity

Fadi Dornaika, Ahmad Khoder

Auto-TLDR; Robust Discriminant Analysis with Feature Selection and Inter-class Sparsity (RDA_FSIS)

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Feature extraction methods have been successfully applied to many real-world applications. The classical Linear Discriminant Analysis (LDA) and its variants are widely used as feature extraction methods. Although they have been used for different classification tasks, these methods have some shortcomings. The main one is that the projection axes obtained are not informative about the relevance of original features. In this paper, we propose a linear embedding method that merges two interesting properties: Robust LDA and inter-class sparsity. Furthermore, the targeted projection transformation focuses on the most discriminant original features. The proposed method is called Robust Discriminant Analysis with Feature Selection and Inter-class Sparsity (RDA_FSIS). Two kinds of sparsity are explicitly included in the proposed model. The first kind is obtained by imposing the $\ell_{2,1}$ constraint on the projection matrix in order to perform feature ranking. The second kind is obtained by imposing the inter-class sparsity constraint used for getting a common sparsity structure in each class. Comprehensive experiments on five real-world image datasets demonstrate the effectiveness and advantages of our framework over existing linear methods.

Probabilistic Latent Factor Model for Collaborative Filtering with Bayesian Inference

Jiansheng Fang, Xiaoqing Zhang, Yan Hu, Yanwu Xu, Ming Yang, Jiang Liu

Auto-TLDR; Bayesian Latent Factor Model for Collaborative Filtering

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Latent Factor Model (LFM) is one of the most successful methods for Collaborative filtering (CF) in the recommendation system, in which both users and items are projected into a joint latent factor space. Base on matrix factorization applied usually in pattern recognition, LFM models user-item interactions as inner products of factor vectors of user and item in that space and can be efficiently solved by least square methods with optimal estimation. However, such optimal estimation methods are prone to overfitting due to the extreme sparsity of user-item interactions. In this paper, we propose a Bayesian treatment for LFM, named Bayesian Latent Factor Model (BLFM). Based on observed user-item interactions, we build a probabilistic factor model in which the regularization is introduced via placing prior constraint on latent factors, and the likelihood function is established over observations and parameters. Then we draw samples of latent factors from the posterior distribution with Variational Inference (VI) to predict expected value. We further make an extension to BLFM, called BLFMBias, incorporating user-dependent and item-dependent biases into the model for enhancing performance. Extensive experiments on the movie rating dataset show the effectiveness of our proposed models by compared with several strong baselines.

Classification and Feature Selection Using a Primal-Dual Method and Projections on Structured Constraints

Michel Barlaud, Antonin Chambolle, Jean_Baptiste Caillau

Auto-TLDR; A Constrained Primal-dual Method for Structured Feature Selection on High Dimensional Data

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This paper deals with feature selection using supervised classification on high dimensional datasets. A classical approach is to project data on a low dimensional space and classify by minimizing an appropriate quadratic cost. Our first contribution is to introduce a matrix of centers in the definition of this cost. Moreover, as quadratic costs are not robust to outliers, we propose to use an $\ell_1$ cost instead (or Huber loss to mitigate overfitting issues). While control on sparsity is commonly obtained by adding an $\ell_1$ constraint on the vectorized matrix of weights used for projecting the data, our second contribution is to enforce structured sparsity. To this end we propose constraints that take into account the matrix structure of the data, based either on the nuclear norm, on the $\ell_{2,1}$ norm, or on the $\ell_{1,2}$ norm for which we provide a new projection algorithm. We optimize simultaneously the projection matrix and the matrix of centers thanks to a new tailored constrained primal-dual method. The primal-dual framework is general enough to encompass the various robust losses and structured constraints we use, and allows a convergence analysis. We demonstrate the effectiveness of the approach on three biological datasets. Our primal-dual method with robust losses, adaptive centers and structured constraints does significantly better than classical methods, both in terms of accuracy and computational time.

Fast Multi-Level Foreground Estimation

Thomas Germer, Tobias Uelwer, Stefan Conrad, Stefan Harmeling

Auto-TLDR; Fur foreground estimation given the alpha matte

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Alpha matting aims to estimate the translucency of an object in a given image. The resulting alpha matte describes pixel-wise to what amount foreground and background colors contribute to the color of the composite image. While most methods in literature focus on estimating the alpha matte, the process of estimating the foreground colors given the input image and its alpha matte is often neglected, although foreground estimation is an essential part of many image editing workflows. In this work, we propose a novel method for foreground estimation given the alpha matte. We demonstrate that our fast multi-level approach yields results that are comparable with the state-of-the-art while outperforming those methods in computational runtime and memory usage.