In the context of supervised learning, meta learning uses features, metadata and other information to learn about the difficulty, behavior, or composition of the problem. Using this knowledge can be useful to contextualize classifier results or allow for targeted decisions about future data sampling. In this paper, we are specifically interested in learning the Bayes error rate (BER) based on a labeled data sample. Providing a tight bound on the BER that is also feasible to estimate has been a challenge. Previous work~\cite{BerishaICassp2016} has shown that a pairwise bound based on the sum of Henze-Penrose (HP) divergence over label pairs can be directly estimated using a sum of Friedman-Rafsky (FR) multivariate run test statistics. However, in situations in which the dataset and number of classes are large, this bound is computationally infeasible to calculate and may not be tight. Other multi-class bounds also suffer from computationally complex estimation procedures. In this paper, we present a generalized HP divergence measure that allows us to estimate the Bayes error rate with log-linear computation. We prove that the proposed bound is tighter than both the pairwise method and a bound proposed by Lin \cite{Lin1991}. We also empirically show that these bounds are close to the BER. We illustrate the proposed method on the MNIST dataset, and show its utility for the evaluation of feature reduction strategies. We further demonstrate an approach for evaluation of deep learning architectures using the proposed bounds.

Several datasets exist which contain annotated information of individuals trajectories. Such datasets are vital for many real-world applications, including trajectory prediction and autonomous navigation. One prominent dataset currently in use is the Stanford Drone Dataset (SDD). Despite its prominence, discussion surrounding the characteristics of this dataset is insufficient. We demonstrate how this insufficiency reduces the information available to users and can impact performance. Our contributions include the outlining of key characteristics in the SDD, employment of an information-theoretic measure and custom metric to clearly visualize those characteristics, the implementation of the PECNet and Y-Net trajectory prediction models to demonstrate the outlined characteristics impact on predictive performance, and lastly we provide a comparison between the SDD and Intersection Drone (inD) Dataset. Our analysis of the SDDs key characteristics is important because without adequate information about available datasets a users ability to select the most suitable dataset for their methods, to reproduce one anothers results, and to interpret their own results are hindered. The observations we make through this analysis provide a readily accessible and interpretable source of information for those planning to use the SDD. Our intention is to increase the performance and reproducibility of methods applied to this dataset going forward, while also clearly detailing less obvious features of the dataset for new users.

In general, deep neural network (DNN) pruning methods fall into two categories: 1) weight-based deterministic constraints and 2) probabilistic frameworks. While each approach has its merits and limitations, there are a set of common practical issues such as trial-and-error to analyze sensitivity and hyper-parameters to prune DNNs, which plague them both. In this work, we propose a new single-shot, fully automated pruning algorithm called slimming neural networks using adaptive connectivity scores (). Our proposed approach combines a probabilistic pruning framework with constraints on the underlying weight matrices, via a novel connectivity measure, at multiple levels to capitalize on the strengths of both approaches while solving their deficiencies. In, we propose a fast hash-based estimator of adaptive conditional mutual information (ACMI), that uses a weight-based scaling criterion, to evaluate the connectivity between filters and prune unimportant ones. To automatically determine the limit up to which a layer can be pruned, we propose a set of operating constraints that jointly define the upper pruning percentage limits across all the layers in a deep network. Finally, we define a novel sensitivity criterion for filters that measures the strength of their contributions to the succeeding layer and highlights critical filters that need to be completely protected from pruning. Through our experimental validation, we show that is faster by over 17 $\times$ the nearest comparable method and is the state-of-the-art single-shot pruning method across four standard Dataset-DNN pruning benchmarks: CIFAR10-VGG16, CIFAR10-ResNet56, CIFAR10-MobileNetv2, and ILSVRC2012-ResNet50.

Graph summarization is the problem of producing smaller graph representations of an input graph dataset, in such a way that the smaller compressed graphs capture relevant structural information for downstream tasks. One of the recent graph summarization methods formulates an optimal transport-based framework that allows prior information about node, edge, and attribute importance to be incorporated into the graph summarization process. However, very little is known about the statistical properties of this framework. To elucidate this question, we consider the problem of supervised graph summarization, wherein by using information theoretic measures we seek to preserve relevant information about a class label. To gain a theoretical perspective on the supervised summarization problem itself, we first formulate it in terms of maximizing the Shannon mutual information between the summarized graph and the class label. We show an NP-hardness of approximation result for this problem, thereby constraining what one should expect from proposed solutions. We then propose a summarization method that incorporates mutual information estimates between random variables associated with sample graphs and class labels into the optimal transport compression framework. We empirically show performance improvements over previous works in terms of classification accuracy and time on synthetic and certain real datasets. We also theoretically explore the limitations of the optimal transport approach for the supervised summarization problem and we show that it fails to satisfy a certain desirable information monotonicity property.

This paper proposes a geometric estimator of dependency between a pair of multivariate random variables. The proposed estimator of dependency is based on a randomly permuted geometric graph (the minimal spanning tree) over the two multivariate samples. This estimator converges to a quantity that we call the geometric mutual information (GMI), which is equivalent to the Henze–Penrose divergence. between the joint distribution of the multivariate samples and the product of the marginals. The GMI has many of the same properties as standard MI but can be estimated from empirical data without density estimation; making it scalable to large datasets. The proposed empirical estimator of GMI is simple to implement, involving the construction of an minimal spanning tree (MST) spanning over both the original data and a randomly permuted version of this data. We establish asymptotic convergence of the estimator and convergence rates of the bias and variance for smooth multivariate density functions belonging to a Hölder class. We demonstrate the advantages of our proposed geometric dependency estimator in a series of experiments.