Related papers: Characterizing Logarithmic Bregman Functions
The distinguishability quantified by information measures after being processed by a private mechanism has been a useful tool in studying various statistical and operational tasks while ensuring privacy. To this end, standard…
Dynamic Mode Decomposition (DMD) is a popular data-driven analysis technique used to decompose complex, nonlinear systems into a set of modes, revealing underlying patterns and dynamics through spectral analysis. This review presents a…
In this paper, we study two problems: (1) estimation of a $d$-dimensional log-concave distribution and (2) bounded multivariate convex regression with random design with an underlying log-concave density or a compactly supported…
Several recent empirical studies demonstrate that important machine learning tasks, e.g., training deep neural networks, exhibit low-rank structure, where the loss function varies significantly in only a few directions of the input space.…
We consider two parametrized random digraph families, namely, proportional-edge and central similarity proximity catch digraphs (PCDs) and compare the performance of these two PCD families in testing spatial point patterns. These PCD…
While likelihood-based inference and its variants provide a statistically efficient and widely applicable approach to parametric inference, their application to models involving intractable likelihoods poses challenges. In this work, we…
The paper provides a thorough investigation of Direct loss minimization (DLM), which optimizes the posterior to minimize predictive loss, in sparse Gaussian processes. For the conjugate case, we consider DLM for log-loss and DLM for square…
The past few years have seen impressive progress in the development of deep generative models capable of producing high-dimensional, complex, and photo-realistic data. However, current methods for evaluating such models remain incomplete:…
We approximate a given rational spectral density by one that is consistent with prescribed second-order statistics. Such an approximation is obtained by minimizing a suitable distance from the given spectrum and under the constraints…
Despite many advances in computational modeling of protein structures, these methods have not been widely utilized by experimental structural biologists. Two major obstacles are preventing the transition from a purely-experimental to a…
Neural networks (NNs) achieve outstanding performance in many domains; however, their decision processes are often opaque and their inference can be computationally expensive in resource-constrained environments. We recently proposed…
We study when low coordinate degree functions (LCDF) -- linear combinations of functions depending on small subsets of entries of a vector -- can hypothesis test between high-dimensional probability measures. These functions are a…
Exponential families and mixture families are parametric probability models that can be geometrically studied as smooth statistical manifolds with respect to any statistical divergence like the Kullback-Leibler (KL) divergence or the…
Low density generator matrix (LDGM) codes have an acceptable performance under iterative decoding algorithms. This idea is used to construct a class of lattices with relatively good performance and low encoding and decoding complexity. To…
Kullback-Leibler divergence (KL) regularization is widely used in reinforcement learning, but it becomes infinite under support mismatch and can degenerate in low-noise limits. Utilizing a unified information-geometric framework, we…
A basic model in sequential decision making is the Markov decision process (MDP), which is extended to Robust MDPs (RMDPs) by allowing uncertainty in transition probabilities and optimizing against the worst-case transition probabilities…
Measuring the in-context computational effort of language models is a key challenge, as metrics like next-token loss fail to capture reasoning complexity. Prior methods based on latent state compressibility can be invasive and unstable. We…
We consider the problem of simultaneous variable selection and estimation of the corresponding regression coefficients in an ultra-high dimensional linear regression models, an extremely important problem in the recent era. The adaptive…
We derive exact analytic solutions for density and velocity fields to all orders in Eulerian standard perturbation theory for $\Lambda$CDM cosmology. In particular, we show that density and velocity field kernels can be written in a…
Bayesian learning has been recently considered as an effective means of accounting for uncertainty in trained deep network parameters. This is of crucial importance when dealing with small or sparse training datasets. On the other hand,…