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Relative Feature Importance

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

Auto-TLDR; Relative Feature Importance for Interpretable Machine Learning

Abstract Slides

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.

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A Multilinear Sampling Algorithm to Estimate Shapley Values

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

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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

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

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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.

Bayesian Active Learning for Maximal Information Gain on Model Parameters

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Auto-TLDR; Bayesian assumptions for Bayesian classification

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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.

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

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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

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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.

On Learning Random Forests for Random Forest Clustering

Manuele Bicego, Francisco Escolano

Auto-TLDR; Learning Random Forests for Clustering

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In this paper we study the poorly investigated problem of learning Random Forests for distance-based Random Forest clustering. We studied both classic schemes as well as alternative approaches, novel in this context. In particular, we investigated the suitability of Gaussian Density Forests, Random Forests specifically designed for density estimation. Further, we introduce a novel variant of Random Forest, based on an effective non parametric by-pass estimator of the Renyi entropy, which can be useful when the parametric assumption is too strict. An empirical evaluation involving different datasets and different RF-clustering strategies confirms that the learning step is crucial for RF-clustering. We also present a set of practical guidelines useful to determine the most suitable variant of RF-clustering according to the problem under examination.

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.

Multi-annotator Probabilistic Active Learning

Marek Herde, Daniel Kottke, Denis Huseljic, Bernhard Sick

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

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Algorithm Recommendation for Data Streams

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Auto-TLDR; Meta-Learning for Algorithm Selection in Time-Changing Data Streams

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In the last decades, many companies are taking advantage of massive data generation at high frequencies through knowledge discovery to identify valuable information. Machine learning techniques can be employed for knowledge discovery, since they are able to extract patterns from data and induce models to predict future events. However, dynamic and evolving environments generate streams of data that usually are non-stationary. Models induced in these scenarios may perish over time due to seasonality or concept drift. The periodic retraining could help but the fixed algorithm's hypothesis space could no longer be appropriate. An alternative solution is to use meta-learning for periodic algorithm selection in time-changing environments, choosing the bias that best suits the current data. In this paper, we present an enhanced framework for data streams algorithm selection based on MetaStream. Our approach uses meta-learning and incremental learning to actively select the best algorithm for the current concept in a time-changing. Different from previous works, a set of cutting edge meta-features and an incremental learning approach in the meta-level based on LightGBM are used. The results show that this new strategy can improve the recommendation of the best algorithm more accurately in time-changing data.

Learning Parameter Distributions to Detect Concept Drift in Data Streams

Johannes Haug, Gjergji Kasneci

Auto-TLDR; A novel framework for the detection of concept drift in streaming environments

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Data distributions in streaming environments are usually not stationary. In order to maintain a high predictive quality at all times, online learning models need to adapt to distributional changes, which are known as concept drift. The timely and robust identification of concept drift can be difficult, as we never have access to the true distribution of streaming data. In this work, we propose a novel framework for the detection of real concept drift, called ERICS. By treating the parameters of a predictive model as random variables, we show that concept drift corresponds to a change in the distribution of optimal parameters. To this end, we adopt common measures from information theory. The proposed framework is completely model-agnostic. By choosing an appropriate base model, ERICS is also capable to detect concept drift at the input level, which is a significant advantage over existing approaches. An evaluation on several synthetic and real-world data sets suggests that the proposed framework identifies concept drift more effectively and precisely than various existing works.

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.

Interpolation in Auto Encoders with Bridge Processes

Carl Ringqvist, Henrik Hult, Judith Butepage, Hedvig Kjellstrom

Auto-TLDR; Stochastic interpolations from auto encoders trained on flattened sequences

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Auto encoding models have been extensively studied in recent years. They provide an efficient framework for sample generation, as well as for analysing feature learning. Furthermore, they are efficient in performing interpolations between data-points in semantically meaningful ways. In this paper, we introduce a method for generating sequence samples from auto encoders trained on flattened sequences (e.g video sample from auto encoders trained to generate a video frame); as well as a canonical, dimension independent method for generating stochastic interpolations. The distribution of interpolation paths is represented as the distribution of a bridge process constructed from an artificial random data generating process in the latent space, having the prior distribution as its invariant distribution.

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

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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.

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.

Graph Discovery for Visual Test Generation

Neil Hallonquist, Laurent Younes, Donald Geman

Auto-TLDR; Visual Question Answering over Graphs: A Probabilistic Framework for VQA

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We consider the problem of uncovering an unknown attributed graph, where both its edges and vertices are hidden from view, through a sequence of binary questions about it. In order to select questions efficiently, we define a probability distribution over graphs, with randomness not just over edges, but over vertices as well. We then sequentially select questions so as to: (1) minimize the expected entropy of the random graph, given the answers to the previous questions in the sequence; and (2) to instantiate the vertices that compose the graph. We propose some basic question spaces, from which to select questions, that vary in their capacity. We apply this framework to the problem of test generation in Visual Question Answering (VQA), where semantic questions are used to evaluate vision systems over rich image representations. To do this, we use a restricted question vocabulary, resulting in image representations that take the form of scene graphs; by defining a distribution over them, a consistent set of probabilities is associated with the questions, and used in their selection.

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

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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.

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.

Fingerprints, Forever Young?

Roman Kessler, Olaf Henniger, Christoph Busch

Auto-TLDR; Mated Similarity Scores for Fingerprint Recognition: A Hierarchical Linear Model

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In the present study we analyzed longitudinal fingerprint data of 20 data subjects, acquired over a time span of up to 12 years. Using hierarchical linear modeling, we aimed to delineate mated similarity scores as a function of fingerprint quality and of the time interval between reference and probe images. Our results did not reveal effects on mated similarity scores caused by an increasing time interval across subjects, but rather individual effects on mated similarity scores. The results are in line with the general assumption that the fingerprint as a biometric characteristic and the features extracted from it do not change over the adult life span. However, it contradicts several related studies that reported noticeable template ageing effects. We discuss why different findings regarding ageing of references in fingerprint recognition systems were made.

Decision Snippet Features

Pascal Welke, Fouad Alkhoury, Christian Bauckhage, Stefan Wrobel

Auto-TLDR; Decision Snippet Features for Interpretability

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Decision trees excel at interpretability of their prediction results. To achieve required prediction accuracies, however, often large ensembles of decision trees -- random forests -- are considered, reducing interpretability due to large size. Additionally, their size slows down inference on modern hardware and restricts their applicability in low-memory embedded devices. We introduce \emph{Decision Snippet Features}, which are obtained from small subtrees that appear frequently in trained random forests. We subsequently show that linear models on top of these features achieve comparable and sometimes even better predictive performance than the original random forest, while reducing the model size by up to two orders of magnitude.

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

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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.

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.

On the Global Self-attention Mechanism for Graph Convolutional Networks

Chen Wang, Deng Chengyuan

Auto-TLDR; Global Self-Attention Mechanism for Graph Convolutional Networks

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Applying Global Self-Attention (GSA) mechanism over features has achieved remarkable success on Convolutional Neural Networks (CNNs). However, it is not clear if Graph Convolutional Networks (GCNs) can similarly benefit from such a technique. In this paper, inspired by the similarity between CNNs and GCNs, we study the impact of the Global Self-Attention mechanism on GCNs. We find that consistent with the intuition, the GSA mechanism allows GCNs to capture feature-based vertex relations regardless of edge connections; As a result, the GSA mechanism can introduce extra expressive power to the GCNs. Furthermore, we analyze the impacts of the GSA mechanism on the issues of overfitting and over-smoothing. We prove that the GSA mechanism can alleviate both the overfitting and the over-smoothing issues based on some recent technical developments. Experiments on multiple benchmark datasets illustrate both superior expressive power and less significant overfitting and over-smoothing problems for the GSA-augmented GCNs, which corroborate the intuitions and the theoretical results.

Inferring Functional Properties from Fluid Dynamics Features

Andrea Schillaci, Maurizio Quadrio, Carlotta Pipolo, Marcello Restelli, Giacomo Boracchi

Auto-TLDR; Exploiting Convective Properties of Computational Fluid Dynamics for Medical Diagnosis

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In a wide range of applied problems involving fluid flows, Computational Fluid Dynamics (CFD) provides detailed quantitative information on the flow field, at various levels of fidelity and computational cost. However, CFD alone cannot predict high-level functional properties of the system that are not easily obtained from the equations of fluid motion. In this work, we present a data-driven framework to extract additional information, such as medical diagnostic output, from CFD solutions. The task is made difficult by the huge data dimensionality of CFD, together with the limited amount of training data implied by its high computational cost. By pursuing a traditional ML pipeline of pre-processing, feature extraction, and model training, we demonstrate that informative features can be extracted from CFD data. Two experiments, pertaining to different application domains, support the claim that the convective properties implicit into a CFD solution can be leveraged to retrieve functional information for which an analytical definition is missing. Despite the preliminary nature of our study and the relative simplicity of both the geometrical and CFD models, for the first time we demonstrate that the combination of ML and CFD can diagnose a complex system in terms of high-level functional information.

Generalization Comparison of Deep Neural Networks Via Output Sensitivity

Mahsa Forouzesh, Farnood Salehi, Patrick Thiran

Auto-TLDR; Generalization of Deep Neural Networks using Sensitivity

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Although recent works have brought some insights into the performance improvement of techniques used in state-of-the-art deep-learning models, more work is needed to understand their generalization properties. We shed light on this matter by linking the loss function to the output's sensitivity to its input. We find a rather strong empirical relation between the output sensitivity and the variance in the bias-variance decomposition of the loss function, which hints on using sensitivity as a metric for comparing the generalization performance of networks, without requiring labeled data. We find that sensitivity is decreased by applying popular methods which improve the generalization performance of the model, such as (1) using a deep network rather than a wide one, (2) adding convolutional layers to baseline classifiers instead of adding fully-connected layers, (3) using batch normalization, dropout and max-pooling, and (4) applying parameter initialization techniques.

A Novel Random Forest Dissimilarity Measure for Multi-View Learning

Hongliu Cao, Simon Bernard, Robert Sabourin, Laurent Heutte

Auto-TLDR; Multi-view Learning with Random Forest Relation Measure and Instance Hardness

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Multi-view learning is a learning task in which data is described by several concurrent representations. Its main challenge is most often to exploit the complementarities between these representations to help solve a classification/regression task. This is a challenge that can be met nowadays if there is a large amount of data available for learning. However, this is not necessarily true for all real-world problems, where data are sometimes scarce (e.g. problems related to the medical environment). In these situations, an effective strategy is to use intermediate representations based on the dissimilarities between instances. This work presents new ways of constructing these dissimilarity representations, learning them from data with Random Forest classifiers. More precisely, two methods are proposed, which modify the Random Forest proximity measure, to adapt it to the context of High Dimension Low Sample Size (HDLSS) multi-view classification problems. The second method, based on an Instance Hardness measurement, is significantly more accurate than other state-of-the-art measurements including the original RF Proximity measurement and the Large Margin Nearest Neighbor (LMNN) metric learning measurement.

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

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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.

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.

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

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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.

Probability Guided Maxout

Claudio Ferrari, Stefano Berretti, Alberto Del Bimbo

Auto-TLDR; Probability Guided Maxout for CNN Training

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In this paper, we propose an original CNN training strategy that brings together ideas from both dropout-like regularization methods and solutions that learn discriminative features. We propose a dropping criterion that, differently from dropout and its variants, is deterministic rather than random. It grounds on the empirical evidence that feature descriptors with larger $L2$-norm and highly-active nodes are strongly correlated to confident class predictions. Thus, our criterion guides towards dropping a percentage of the most active nodes of the descriptors, proportionally to the estimated class probability. We simultaneously train a per-sample scaling factor to balance the expected output across training and inference. This further allows us to keep high the descriptor's L2-norm, which we show enforces confident predictions. The combination of these two strategies resulted in our ``Probability Guided Maxout'' solution that acts as a training regularizer. We prove the above behaviors by reporting extensive image classification results on the CIFAR10, CIFAR100, and Caltech256 datasets.

Adaptive Matching of Kernel Means

Miao Cheng, Xinge You

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

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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.

Dependently Coupled Principal Component Analysis for Bivariate Inversion Problems

Navdeep Dahiya, Yifei Fan, Samuel Bignardi, Tony Yezzi, Romeil Sandhu

Auto-TLDR; Asymmetric Principal Component Analysis between Paired Data in an Asymmetric manner

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Principal Component Analysis (PCA) is a widely used technique for dimensionality reduction in various problem domains including data compression, image processing, visualization, exploratory data analysis, pattern recognition, time series prediction and machine learning. Often, data is presented in a correlated paired manner such there exists observable and correlated unobservable measurements. Unfortunately, traditional PCA techniques generally fail to optimally capture the leverageable correlations between such paired data as it does not yield a maximally correlated basis between the observable and unobservable counterparts. This instead is the objective of Canonical Correlation Analysis (and the more general Partial Least Squares methods); however, such techniques are still symmetric in maximizing correlation (covariance for PLSR) over all choices of basis for both datasets without differentiating between observable and unobservable variables (except for the regression phase of PLSR). Further, these methods deviate from PCA's formulation objective to minimize approximation error, seeking instead to maximize correlation or covariance. While these are sensible optimization objectives, they are not equivalent to error minimization. We therefore introduce a new method of leveraging PCA between paired datasets in an asymmetric manner which is optimal with respect to approximation error during training. We generate an asymmetrically paired basis for which we relax orthogonality constraints on the orthogonality in decomposing unreliable unobservable measurements. In doing so, this allows us to optimally capture the variations of the observable data while conditionally minimizing the expected prediction error for the unobservable component. We show preliminary results that demonstrate improved learning of our proposed method compared to that of traditional techniques.

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.

Making Every Label Count: Handling Semantic Imprecision by Integrating Domain Knowledge

Clemens-Alexander Brust, Björn Barz, Joachim Denzler

Auto-TLDR; Class Hierarchies for Imprecise Label Learning and Annotation eXtrapolation

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Noisy data, crawled from the web or supplied by volunteers such as Mechanical Turkers or citizen scientists, is considered an alternative to professionally labeled data. There has been research focused on mitigating the effects of label noise. It is typically modeled as inaccuracy, where the correct label is replaced by an incorrect label from the same set. We consider an additional dimension of label noise: imprecision. For example, a non-breeding snow bunting is labeled as a bird. This label is correct, but not as precise as the task requires. Standard softmax classifiers cannot learn from such a weak label because they consider all classes mutually exclusive, which non-breeding snow bunting and bird are not. We propose CHILLAX (Class Hierarchies for Imprecise Label Learning and Annotation eXtrapolation), a method based on hierarchical classification, to fully utilize labels of any precision. Experiments on noisy variants of NABirds and ILSVRC2012 show that our method outperforms strong baselines by as much as 16.4 percentage points, and the current state of the art by up to 3.9 percentage points.

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.

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

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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.

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

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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.

Automatic Classification of Human Granulosa Cells in Assisted Reproductive Technology Using Vibrational Spectroscopy Imaging

Marina Paolanti, Emanuele Frontoni, Giorgia Gioacchini, Giorgini Elisabetta, Notarstefano Valentina, Zacà Carlotta, Carnevali Oliana, Andrea Borini, Marco Mameli

Auto-TLDR; Predicting Oocyte Quality in Assisted Reproductive Technology Using Machine Learning Techniques

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In the field of reproductive technology, the biochemical composition of female gametes has been successfully investigated with the use of vibrational spectroscopy. Currently, in assistive reproductive technology (ART), there are no shared criteria for the choice of oocyte, and automatic classification methods for the best quality oocytes have not yet been applied. In this paper, considering the lack of criteria in Assisted Reproductive Technology (ART), we use Machine Learning (ML) techniques to predict oocyte quality for a successful pregnancy. To improve the chances of successful implantation and minimize any complications during the pregnancy, Fourier transform infrared microspectroscopy (FTIRM) analysis has been applied on granulosa cells (GCs) collected along with the oocytes during oocyte aspiration, as it is routinely done in ART, and specific spectral biomarkers were selected by multivariate statistical analysis. A proprietary biological reference dataset (BRD) was successfully collected to predict the best oocyte for a successful pregnancy. Personal health information are stored, maintained and backed up using a cloud computing service. Using a user-friendly interface, the user will evaluate whether or not the selected oocyte will have a positive result. This interface includes a dashboard for retrospective analysis, reporting, real-time processing, and statistical analysis. The experimental results are promising and confirm the efficiency of the method in terms of classification metrics: precision, recall, and F1-score (F1) measures.

Directionally Paired Principal Component Analysis for Bivariate Estimation Problems

Navdeep Dahiya, Yifei Fan, Samuel Bignardi, Tony Yezzi, Romeil Sandhu

Auto-TLDR; Asymmetrically-Paired Principal Component Analysis for Linear Dimension-Reduction

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We propose Asymmetrically-Paired Principal Component Analysis (APPCA), a novel linear dimension-reduction model for estimating coupled yet partially available variable sets. Unlike partial least square methods (e.g., partial least square regression and canonical correlation analysis) which maximize correlation/covariance between the two datasets, our APPCA directly minimizes, either conditionally or unconditionally, the reconstruction and prediction errors for the observable and unobservable part, respectively. We demonstrate the optimality of the proposed APPCA approach, we compare and evaluate relevant linear cross-decomposition methods with data reconstruction and prediction experiments on synthetic Gaussian data, multi-target regression datasets and single-channel image datasets. Results show that when only a single pair of bases is allowed, the conditional APPCA achieves lowest reconstruction error on the observable part and the total variable sets as a whole, meanwhile the unconditional APPCA reaches lowest prediction errors on the unobservable part. When extra budget is allowed for the PCA basis of the observable part, one can reach optimal solution using a combine method: standard PCA for the observable part and unconditional APPCA for the unobservable part.

Verifying the Causes of Adversarial Examples

Honglin Li, Yifei Fan, Frieder Ganz, Tony Yezzi, Payam Barnaghi

Auto-TLDR; Exploring the Causes of Adversarial Examples in Neural Networks

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The robustness of neural networks is challenged by adversarial examples that contain almost imperceptible perturbations to inputs which mislead a classifier to incorrect outputs in high confidence. Limited by the extreme difficulty in examining a high-dimensional image space thoroughly, research on explaining and justifying the causes of adversarial examples falls behind studies on attacks and defenses. In this paper, we present a collection of potential causes of adversarial examples and verify (or partially verify) them through carefully-designed controlled experiments. The major causes of adversarial examples include model linearity, one-sum constraint, and geometry of the categories. To control the effect of those causes, multiple techniques are applied such as $L_2$ normalization, replacement of loss functions, construction of reference datasets, and novel models using multi-layer perceptron probabilistic neural networks (MLP-PNN) and density estimation (DE). Our experiment results show that geometric factors tend to be more direct causes and statistical factors magnify the phenomenon, especially for assigning high prediction confidence. We hope this paper will inspire more studies to rigorously investigate the root causes of adversarial examples, which in turn provide useful guidance on designing more robust models.

Hierarchical Routing Mixture of Experts

Wenbo Zhao, Yang Gao, Shahan Ali Memon, Bhiksha Raj, Rita Singh

Auto-TLDR; A Binary Tree-structured Hierarchical Routing Mixture of Experts for Regression

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In regression tasks the distribution of the data is often too complex to be fitted by a single model. In contrast, partition-based models are developed where data is divided and fitted by local models. These models partition the input space and do not leverage the input-output dependency of multimodal-distributed data, and strong local models are needed to make good predictions. Addressing these problems, we propose a binary tree-structured hierarchical routing mixture of experts (HRME) model that has classifiers as non-leaf node experts and simple regression models as leaf node experts. The classifier nodes jointly soft-partition the input-output space based on the natural separateness of multimodal data. This enables simple leaf experts to be effective for prediction. Further, we develop a probabilistic framework for the HRME model, and propose a recursive Expectation-Maximization (EM) based algorithm to learn both the tree structure and the expert models. Experiments on a collection of regression tasks validate the effectiveness of our method compared to a variety of other regression models.

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.

Naturally Constrained Online Expectation Maximization

Daniela Pamplona, Antoine Manzanera

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

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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.

Overcoming Noisy and Irrelevant Data in Federated Learning

Tiffany Tuor, Shiqiang Wang, Bong Jun Ko, Changchang Liu, Kin K Leung

Auto-TLDR; Distributedly Selecting Relevant Data for Federated Learning

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Many image and vision applications require a large amount of data for model training. Collecting all such data at a central location can be challenging due to data privacy and communication bandwidth restrictions. Federated learning is an effective way of training a machine learning model in a distributed manner from local data collected by client devices, which does not require exchanging the raw data among clients. A challenge is that among the large variety of data collected at each client, it is likely that only a subset is relevant for a learning task while the rest of data has a negative impact on model training. Therefore, before starting the learning process, it is important to select the subset of data that is relevant to the given federated learning task. In this paper, we propose a method for distributedly selecting relevant data, where we use a benchmark model trained on a small benchmark dataset that is task-specific, to evaluate the relevance of individual data samples at each client and select the data with sufficiently high relevance. Then, each client only uses the selected subset of its data in the federated learning process. The effectiveness of our proposed approach is evaluated on multiple real-world image datasets in a simulated system with a large number of clients, showing up to 25% improvement in model accuracy compared to training with all data.

Attack-Agnostic Adversarial Detection on Medical Data Using Explainable Machine Learning

Matthew Watson, Noura Al Moubayed

Auto-TLDR; Explainability-based Detection of Adversarial Samples on EHR and Chest X-Ray Data

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Explainable machine learning has become increasingly prevalent, especially in healthcare where explainable models are vital for ethical and trusted automated decision making. Work on the susceptibility of deep learning models to adversarial attacks has shown the ease of designing samples to mislead a model into making incorrect predictions. In this work, we propose an explainability-based method for the accurate detection of adversarial samples on two datasets with different complexity and properties: Electronic Health Record (EHR) and chest X-ray (CXR) data. On the MIMIC-III and Henan-Renmin EHR datasets, we report a detection accuracy of 77% against the Longitudinal Adversarial Attack. On the MIMIC-CXR dataset, we achieve an accuracy of 88%; significantly improving on the state of the art of adversarial detection in both datasets by over 10% in all settings. We propose an anomaly detection based method using explainability techniques to detect adversarial samples which is able to generalise to different attack methods without a need for retraining.

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

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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.

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.

Using Meta Labels for the Training of Weighting Models in a Sample-Specific Late Fusion Classification Architecture

Peter Bellmann, Patrick Thiam, Friedhelm Schwenker

Auto-TLDR; A Late Fusion Architecture for Multiple Classifier Systems

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The performance of multiple classifier systems can be significantly improved by the use of intelligent classifier combination approaches. In this study, we introduce a novel late fusion architecture, which can be interpreted as a combination of the well-known mixture of experts and stacked generalization methods. Our proposed method aggregates the outputs of classification models and corresponding sample-specific weighting models. A special feature of our proposed architecture is that each weighting model is trained on an individual set of meta labels. Using individual sets of meta labels allows each weighting model to separate regions, on which the predictions of the corresponding classification model can be associated to an estimated confidence value. We test our proposed architecture on a set of publicly available databases, including different benchmark data sets. The experimental evaluation shows the effectiveness and potential of our proposed method. Moreover, we discuss different approaches for further improvement of our proposed architecture.