The existence of adversarial examples capable of fooling trained neural network classifiers calls for a much better understanding of possible attacks, in order to guide the development of safeguards against them. It includes attack methods in the highly challenging non-interactive blackbox setting, where adversarial attacks are generated without any access, including queries, to the target model. Prior works in this setting have relied mainly on algorithmic innovations derived from empirical observations (e.g., that momentum helps), and the field currently lacks a firm theoretical basis for understanding transferability in adversarial attacks. In this work, we address this gap and lay the theoretical foundations for crafting transferable adversarial examples to entire function classes. We introduce Adversarial Examples Games (AEG), a novel framework that models adversarial examples as two-player min-max games between an attack generator and a representative classifier. We prove that the saddle point of an AEG game corresponds to a generating distribution of adversarial examples against entire function classes. Training the generator only requires the ability to optimize a representative classifier from a given hypothesis class, enabling BlackBox transfer to unseen classifiers from the same class. We demonstrate the efficacy of our approach on the MNIST and CIFAR-10 datasets against both undefended and robustified models, achieving competitive performance with state-of-the-art BlackBox transfer approaches.

Converging evidence shows that disease-relevant brain alterations do not appear in random brain locations, instead, its spatial pattern follows large scale brain networks. In this context, a powerful network analysis approach with a mathematical foundation is indispensable to understand the mechanism of neuropathological events spreading throughout the brain. Indeed, the topology of each brain network is governed by its native harmonic waves, which are a set of orthogonal bases derived from the Eigen-system of the underlying Laplacian matrix. To that end, we propose a novel connectome harmonic analysis framework to provide enhanced mathematical insights by detecting frequency-based alterations relevant to brain disorders. The backbone of our framework is a novel manifold algebra appropriate for inference across harmonic waves that overcomes the limitations of using classic Euclidean operations on irregular data structures. The individual harmonic difference is measured by a set of common harmonic waves learned from a population of individual Eigen systems, where each native Eigen-system is regarded as a sample drawn from the Stiefel manifold. Specifically, a manifold optimization scheme is tailored to find the common harmonic waves which reside at the center of Stiefel manifold. To that end, the common harmonic waves constitute the new neuro-biological bases to understand disease progression. Each harmonic wave exhibits a unique propagation pattern of neuro-pathological burdens spreading across brain networks. The statistical power of our novel connectome harmonic analysis approach is evaluated by identifying frequency-based alterations relevant to Alzheimer's disease, where our learning-based manifold approach discovers more significant and reproducible network dysfunction patterns compared to Euclidian methods.

We present a novel analysis of the expected risk of weighted majority vote in multiclass classification. The analysis takes correlation of predictions by ensemble members into account and provides a bound that is amenable to efficient minimization, which yields improved weighting for the majority vote. We also provide a specialized version of our bound for binary classification, which allows to exploit additional unlabeled data for tighter risk estimation. In experiments, we apply the bound to improve weighting of trees in random forests and show that, in contrast to the commonly used first order bound, minimization of the new bound typically does not lead to degradation of the test error of the ensemble.

While current research has shown the importance of Multi-parametric MRI (mpMRI) in diagnosing prostate cancer (PCa), further investigation is needed for how to incorporate the specific structures of the mpMRI data, such as the regional heterogeneity and between-voxel correlation within a subject. This paper proposes a machine learning-based method for improved voxel-wise PCa classification by taking into account the unique structures of the data. We propose a multi-resolution modeling approach to account for regional heterogeneity, where base learners trained locally at multiple resolutions are combined using the super learner, and account for between-voxel correlation by efficient spatial Gaussian kernel smoothing. The method is flexible in that the super learner framework allows implementation of any classifier as the base learner, and can be easily extended to classifying cancer into more sub-categories. We describe detailed classification algorithm for the binary PCa status, as well as the ordinal clinical significance of PCa for which a weighted likelihood approach is implemented to enhance the detection of the less prevalent cancer categories. We illustrate the advantages of the proposed approach over conventional modeling and machine learning approaches through simulations and application to in vivo data.

Bayesian coresets have emerged as a promising approach for scalable Bayesian inference [22, 12, 13, 11]. The key idea is to select a (weighted) subset of the data such that posterior inference using the selected subset closely approximates posterior inference using the full dataset. This creates a tradeoff, where using Bayesian coresets as opposed to the full dataset exchanges approximation accuracy for computational speedups. We study Bayesian coresets as they are easy to implement, effective in practice, and come with useful theoretical guarantees that relate the coreset size with the approximation quality. The main technical challenge in the Bayesian coreset problem lies in handling the combinatorial constraints - we desire to select a few data points out of many as the coreset. The state of the art approaches rely on two ideas: convexification and greedy methods. In convexification [13], the sparsity constraint - i.e., selection of k data samples - is relaxed into a convex l

Existing domain adaptation methods aim to reduce the distributional difference between the source and target domains and respect their specific discriminative information, by establishing the Maximum Mean Discrepancy (MMD) and the discriminative distances. However, they usually accumulate to consider those statistics and deal with their relationships by estimating parameters blindly. This paper theoretically proves two essential facts: 1) minimizing the MMD equals to maximize the source and target intra-class distances respectively but jointly minimize their variance with some implicit weights, so that the feature discriminability degrades; 2) the relationship between the intra-class and inter-class distances is as one falls, another rises. Based on this, we propose a novel discriminative MMD. On one hand, we consider the intra-class and inter-class distances alone to remove a redundant parameter, and the revealed weights provide their approximate optimal ranges. On the other hand, we design two different strategies to boost the feature discriminability: 1) we directly impose a trade-off parameter on the implicit intra-class distance in MMD to regulate its change; 2) we impose the similar weights revealed in MMD on inter-class distance and maximize it, then a balanced factor could be introduced to quantitatively leverage the relative importance between the feature transferability and its discriminability. The experiments on several benchmark datasets not only prove the validity of theoretical results but also demonstrate that our approach could perform better than the comparative state-of-art methods substantially.

The recently proposed Thermodynamic Variational Objective (TVO) leverages thermodynamic integration to provide a family of variational inference objectives, which both tighten and generalize the ubiquitous Evidence Lower Bound (ELBO). However, the tightness of TVO bounds was not previously known, an expensive grid search was used to choose a "schedule" of intermediate distributions, and model learning suffered with ostensibly tighter bounds. In this work, we propose an exponential family interpretation of the geometric mixture curve underlying the TVO and various path sampling methods, which allows us to characterize the gap in TVO likelihood bounds as a sum of KL divergences. We propose to choose intermediate distributions using equal spacing in the moment parameters of our exponential family, which matches grid search performance and allows the schedule to adaptively update over the course of training. Finally, we derive a doubly reparameterized gradient estimator which improves model learning and allows the TVO to benefit from more refined bounds. To further contextualize our contributions, we provide a unified framework for understanding thermodynamic integration and the TVO using Taylor series remainders.

Financial transactions constitute connections between entities and through these connections a large scale heterogeneous weighted graph is formulated. In this labyrinth of interactions that are continuously updated, there exists a variety of similarity-based patterns that can provide insights into the dynamics of the financial system. With the current work, we propose the application of Graph Representation Learning in a scalable dynamic setting as a means of capturing these patterns in a meaningful and robust way. We proceed to perform a rigorous qualitative analysis of the latent trajectories to extract real world insights from the proposed representations and their evolution over time that is to our knowledge the first of its kind in the financial sector. Shifts in the latent space are associated with known economic events and in particular the impact of the recent Covid-19 pandemic to consumer patterns. Capturing such patterns indicates the value added to financial modeling through the incorporation of latent graph representations.

Constant step-size Stochastic Gradient Descent exhibits two phases: a transient phase during which iterates make fast progress towards the optimum, followed by a stationary phase during which iterates oscillate around the optimal point. In this paper, we show that efficiently detecting this transition and appropriately decreasing the step size can lead to fast convergence rates. We analyse the classical statistical test proposed by Pflug (1983), based on the inner product between consecutive stochastic gradients. Even in the simple case where the objective function is quadratic we show that this test cannot lead to an adequate convergence diagnostic. We then propose a novel and simple statistical procedure that accurately detects stationarity and we provide experimental results showing state-of-the-art performance on synthetic and real-world datasets.

This work elaborates on the important problem of (1) designing optimal randomized routing policies for reaching a target node t from a source note s on a weighted directed graph G and (2) defining distance measures between nodes interpolating between the least cost (based on optimal movements) and the commute-cost (based on a random walk on G), depending on a temperature parameter T. To this end, the randomized shortest path formalism (RSP, [2,99,124]) is rephrased in terms of Tsallis divergence regularization, instead of Kullback-Leibler divergence. The main consequence of this change is that the resulting routing policy (local transition probabilities) becomes sparser when T decreases, therefore inducing a sparse random walk on G converging to the least-cost directed acyclic graph when T tends to 0. Experimental comparisons on node clustering and semi-supervised classification tasks show that the derived dissimilarity measures based on expected routing costs provide state-of-the-art results. The sparse RSP is therefore a promising model of movements on a graph, balancing sparse exploitation and exploration in an optimal way.