arXiv research

We prove lognormal distribution for symmetric perceptron model, solving key conjectures.

STICC clusters geographic objects considering both spatial contiguity and attributes.

Using ideas from shape theory we embed the coarse category of metric spaces into the category of direct sequences of simplicial complexes with bonding maps being simplicial. Two direct sequences of simplicial complexes are equivalent if one of them can be transformed to the other by contiguous factorizations of bonding…

Sharp thresholds and contiguity for community detection in contextual SBM.

Regionalization is the task of dividing up a landscape into homogeneous patches with similar properties. Although this task has a wide range of applications, it has two notable challenges. First, it is assumed that the resulting regions are both homogeneous and spatially contiguous. Second, it is well-recognized that l…

Scalable method for regionalizing and extracting temporal patterns from time series data.

Hyperspectral imaging is a powerful technology that is plagued by large dimensionality. Herein, we explore a way to combat that hindrance via non-contiguous and contiguous (simpler to realize sensor) band grouping for dimensionality reduction. Our approach is different in the respect that it is flexible and it follows …

New insights into bias-variance tradeoff for data-driven optimization under local misspecification.

The classic double bubble theorem says that the least-perimeter way to enclose and separate two prescribed volumes in $\mathbb{R}^N$ is the standard double bubble. We seek the optimal double bubble in $\mathbb{R}^N$ with density, which we assume to be strictly log-convex. For $N=1$ we show that the solution is sometime…

Identification of regions of interest (ROI) associated with certain disease has a great impact on public health. Imposing sparsity of pixel values and extracting active regions simultaneously greatly complicate the image analysis. We address these challenges by introducing a novel region-selection penalty in the framew…

We consider the problems of detection and localization of a contiguous block of weak activation in a large matrix, from a small number of noisy, possibly adaptive, compressive (linear) measurements. This is closely related to the problem of compressed sensing, where the task is to estimate a sparse vector using a small…

The paper develops distribution-free methods for ordinal classification.

We present two identities (contiguity relation and variation formula) concerning the volume of a spherically faced simplex in the Euclidean space. These identities are described in terms of Cayley-Menger determinants and their differentials involved with hypersphere arrangements. They are derived as a limit of fundamen…

New method explains computational barriers in high-dimensional statistical models.

Paper proves computational hardness for graph matching and detection problems.

We present a novel statistical inference framework for convex empirical risk minimization, using approximate stochastic Newton steps. The proposed algorithm is based on the notion of finite differences and allows the approximation of a Hessian-vector product from first-order information. In theory, our method efficient…

Complex non-linear interactions between banks and assets we model by two time-dependent Erdős Renyi network models where each node, representing bank, can invest either to a single asset (model I) or multiple assets (model II). We use dynamical network approach to evaluate the collective financial failure---systemic ri…

PatchUp improves CNN robustness with mixed feature blocks.

Study robustness of split conformal prediction under adversarial attacks.

In this paper, we work to construct mosaic representations of knots on the torus, rather than in the plane. This consists of a particular choice of the ambient group, as well as different definitions of contiguous and suitably connected. We present conditions under which mosaic numbers might decrease by this projection…

This paper sharpens privacy guarantees for high-dimensional PCA under differential privacy.

This paper proposes new search algorithms for counterfactual explanations based upon mixed integer programming. We are concerned with complex data in which variables may take any value from a contiguous range or an additional set of discrete states. We propose a novel set of constraints that we refer to as a "mixed pol…

There is a growing interest in joint multi-subject fMRI analysis. The challenge of such analysis comes from inherent anatomical and functional variability across subjects. One approach to resolving this is a shared response factor model. This assumes a shared and time synchronized stimulus across subjects. Such a model…

Functional data analysis involves data described by regular functions rather than by a finite number of real valued variables. While some robust data analysis methods can be applied directly to the very high dimensional vectors obtained from a fine grid sampling of functional data, all methods benefit from a prior simp…

A fundamental problem in network data analysis is to test Erdös-Rényi model $\mathcal{G}\left(n,\frac{a+b}{2n}\right)$ versus a bisection stochastic block model $\mathcal{G}\left(n,\frac{a}{n},\frac{b}{n}\right)$, where $a,b>0$ are constants that represent the expected degrees of the graphs and $n$ denotes the number o…

This paper deals with the notion of a large financial market and the concepts of asymptotic arbitrage and strong asymptotic arbitrage (both of the first kind), introduced by Yu.M. Kabanov and D.O. Kramkov. We show that the arbitrage properties of a large market are completely determined by the asymptotic behavior of th…

We compute exact values respectively bounds of "distances" - in the sense of (transforms of) power divergences and relative entropy - between two discrete-time Galton-Watson branching processes with immigration GWI for which the offspring as well as the immigration is arbitrarily Poisson-distributed (leading to arbitra…

New memory allocation scheme improves image generation performance.

In this paper, we prove than given two cubic knots $K_1$, $K_2$ in $\mathbb{R}^3$, they are isotopic if and only if one can pass from one to the other by a finite sequence of cubulated moves. These moves are analogous to the Reidemeister moves for classical tame knots. We use the fact that a cubic knot is determined by…

Markov regime switching models have been used in numerous empirical studies in economics and finance. However, the asymptotic distribution of the likelihood ratio test statistic for testing the number of regimes in Markov regime switching models has been an unresolved problem. This paper derives the asymptotic distribu…

We give characterizations of asymptotic arbitrage of the first and second kind and of strong asymptotic arbitrage for large financial markets with small proportional transaction costs $\la_n$ on market $n$ in terms of contiguity properties of sequences of equivalent probability measures induced by $\la_n$--consistent p…

Rényi divergence is related to Rényi entropy much like Kullback-Leibler divergence is related to Shannon's entropy, and comes up in many settings. It was introduced by Rényi as a measure of information that satisfies almost the same axioms as Kullback-Leibler divergence, and depends on a parameter that is called its or…

Density-based clustering is the task of discovering high-density regions of entities (clusters) that are separated from each other by contiguous regions of low-density. DBSCAN is, arguably, the most popular density-based clustering algorithm. However, its cluster recovery capabilities depend on the combination of the t…

Interpretable semantic textual similarity (iSTS) task adds a crucial explanatory layer to pairwise sentence similarity. We address various components of this task: chunk level semantic alignment along with assignment of similarity type and score for aligned chunks with a novel system presented in this paper. We propose…

Spotlight method finds hidden errors in deep learning models.

Associating distinct groups of objects (clusters) with contiguous regions of high probability density (high-density clusters), is central to many statistical and machine learning approaches to the classification of unlabelled data. We propose a novel hyperplane classifier for clustering and semi-supervised classificati…

A central problem of random matrix theory is to understand the eigenvalues of spiked random matrix models, introduced by Johnstone, in which a prominent eigenvector (or "spike") is planted into a random matrix. These distributions form natural statistical models for principal component analysis (PCA) problems throughou…

In this paper, we propose a Ward-like hierarchical clustering algorithm including spatial/geographical constraints. Two dissimilarity matrices $D_0$ and $D_1$ are inputted, along with a mixing parameter $α\in [0,1]$. The dissimilarities can be non-Euclidean and the weights of the observations can be non-uniform. The fi…

We study a generalized framework for structured sparsity. It extends the well-known methods of Lasso and Group Lasso by incorporating additional constraints on the variables as part of a convex optimization problem. This framework provides a straightforward way of favouring prescribed sparsity patterns, such as orderin…

Hidden Markov models (HMMs) are one of the most widely used statistical methods for analyzing sequence data. However, the reporting of output from HMMs has largely been restricted to the presentation of the most-probable (MAP) hidden state sequence, found via the Viterbi algorithm, or the sequence of most probable marg…

Training-free looped transformers improve model performance without additional training.

Large-scale trends in urban crime and global terrorism are well-predicted by socio-economic drivers, but focused, event-level predictions have had limited success. Standard machine learning approaches are promising, but lack interpretability, are generally interpolative, and ineffective for precise future interventions…

We study the fundamental limits of detecting the presence of an additive rank-one perturbation, or spike, to a Wigner matrix. When the spike comes from a prior that is i.i.d. across coordinates, we prove that the log-likelihood ratio of the spiked model against the non-spiked one is asymptotically normal below a certai…

Multi-SpaCE generates valid counterfactual explanations for multivariate time series data.

SliceOut speeds up deep learning training without sacrificing accuracy.

Random forest and deep neural network are two schools of effective classification methods in machine learning. While the random forest is robust irrespective of the data domain, the deep neural network has advantages in handling high dimensional data. In view that a differentiable neural decision forest can be added to…

Generative adversarial approach for satellite image time series land cover classification.

Adversarial examples are maliciously perturbed inputs designed to mislead machine learning (ML) models at test-time. They often transfer: the same adversarial example fools more than one model. In this work, we propose novel methods for estimating the previously unknown dimensionality of the space of adversarial inputs…