There is no theory yet as to whydeep neural networks (DNNs from here on) are as effectiveand efficient in practice as they evidently are.

Neural Information Processing Systems http://nips.cc/

We formally introduce the notion of optimal ROC curve over a general model space.

Stochastic neural networks (SNNs) are random functions whose predictions are gained by averaging over multiple realizations.

This paper addresses classification problems with matrix-valued data, which commonly arises in applications such as neuroimaging and signal processing. Building on the assumption that the data from each class follows a matrix normal distribution, we propose a novel extension of Fisher's Linear Discriminant Analysis (LDA) tailored for matrix-valued observations. To effectively capture structural information while maintaining estimation flexibility, we adopt a nonparametric empirical Bayes framework based on Nonparametric Maximum Likelihood Estimation (NPMLE), applied to vectorized and scaled matrices. The NPMLE method has been shown to provide robust, flexible, and accurate estimates for vector-valued data with various structures in the mean vector or covariance matrix. By leveraging its strengths, our method is effectively generalized to the matrix setting, thereby improving classification performance. Through extensive simulation studies and real data applications, including electroencephalography (EEG) and magnetic resonance imaging (MRI) analysis, we demonstrate that the proposed method consistently outperforms existing approaches across a variety of data structures.

For many of the state-of-the-art computer vision algorithms, image segmentation is an important preprocessing step. As such, several image segmentation algorithms have been proposed, however, with certain reservation due to high computational load and many hand-tuning parameters. Correlation clustering, a graphpartitioning algorithm often used in natural language processing and document clustering, has the potential to perform better than previously proposed image segmentation algorithms. We improve the basic correlation clustering formulation by taking into account higher-order cluster relationships. This improves clustering in the presence of local boundary ambiguities. We first apply the pairwise correlation clustering to image segmentation over a pairwise superpixel graph and then develop higher-order correlation clustering over a hypergraph that considers higher-order relations among superpixels. Fast inference is possible by linear programming relaxation, and also effective parameter learning framework by structured support vector machine is possible. Experimental results on various datasets show that the proposed higher-order correlation clustering outperforms other state-of-the-art image segmentation algorithms.

Understanding black-box Machine Learning methods on multidimensional data is a key challenge in Machine Learning. While many powerful Machine Learning methods already exist, these methods are often unexplainable or perform poorly on complex data. This paper proposes visual knowledge discovery approaches based on several forms of lossless General Line Coordinates. These are an expansion of the previously introduced General Line Coordinates Linear and Dynamic Scaffolding Coordinates to produce, explain, and visualize non-linear classifiers with explanation rules. To ensure these non-linear models and rules are accurate, General Line Coordinates Linear also developed new interactive visual knowledge discovery algorithms for finding worst-case validation splits. These expansions are General Line Coordinates non-linear, interactive rules linear, hyperblock rules linear, and worst-case linear. Experiments across multiple benchmark datasets show that this visual knowledge discovery method can compete with other visual and computational Machine Learning algorithms while improving both interpretability and accuracy in linear and non-linear classifications. Major benefits from these expansions consist of the ability to build accurate and highly interpretable models and rules from hyperblocks, the ability to analyze interpretability weaknesses in a model, and the input of expert knowledge through interactive and human-guided visual knowledge discovery methods.

Stochastic neural networks (SNNs) are random functions whose predictions are gained by averaging over multiple realizations. Consequently, a gradient-based adversarial example is calculated based on one set of samples and its classification on another set. In this paper, we derive a sufficient condition for such a stochastic prediction to be robust against a given sample-based attack. This allows us to identify the factors that lead to an increased robustness of SNNs and gives theoretical explanations for: (i) the well known observation, that increasing the amount of samples drawn for the estimation of adversarial examples increases the attack's strength, (ii) why increasing the number of samples during an attack can not fully reduce the effect of stochasticity, (iii) why the sample size during inference does not influence the robustness, and (iv) why a higher gradient variance and a shorter expected value of the gradient relates to a higher robustness. Our theoretical findings give a unified view on the mechanisms underlying previously proposed approaches for increasing attack strengths or model robustness and are verified by an extensive empirical analysis.