arXiv research

A new framework for robust transfer learning that avoids negative transfer in domains with unequal information.

Study exact minimax rates for density estimation over convex classes, extending previous work.

The paper extends statistical estimation techniques under differential privacy.

This paper studies a class of exponential family models whose canonical parameters are specified as linear functionals of an unknown infinite-dimensional slope function. The optimal minimax rates of convergence for slope function estimation are established. The estimators that achieve the optimal rates are constructed …

New framework resolves central limit behavior in differential privacy.

Paper introduces robust deep learning method for handling random data corruption.

The basic model for high-frequency data in finance is considered, where an efficient price process is observed under microstructure noise. It is shown that this nonparametric model is in Le Cam's sense asymptotically equivalent to a Gaussian shift experiment in terms of the square root of the volatility function $σ$. A…

This work explores limits of machine learning robustness against adversarial attacks.

LDP is equivalent to contraction of E_γ-divergence, impacting privacy and utility.

We study local complexity measures for stochastic convex optimization problems, providing a local minimax theory analogous to that of Hájek and Le Cam for classical statistical problems. We give complementary optimality results, developing fully online methods that adaptively achieve optimal convergence guarantees. Our…

"Deep Learning" methods attempt to learn generic features in an unsupervised fashion from a large unlabelled data set. These generic features should perform as well as the best hand crafted features for any learning problem that makes use of this data. We provide a definition of generic features, characterize when it i…

Unified framework for lower bounds in interactive decision making.

Stochastic approximation proves asymptotic normality for non-smooth problems.

Stochastic algo learns from evolving data, achieving optimal performance.

To better understand the interplay of censoring and sparsity we develop finite sample properties of nonparametric Cox proportional hazard's model. Due to high impact of sequencing data, carrying genetic information of each individual, we work with over-parametrized problem and propose general class of group penalties s…

The study examines conditions for achieving a simple lower bound in estimating mean from samples.

Often, high dimensional data lie close to a low-dimensional submanifold and it is of interest to understand the geometry of these submanifolds. The homology groups of a manifold are important topological invariants that provide an algebraic summary of the manifold. These groups contain rich topological information, for…

Blind Source Separation (BSS) has proven to be a powerful tool for the analysis of composite patterns in engineering and science. We introduce Convex Analysis of Mixtures (CAM) for separating non-negative well-grounded sources, which learns the mixing matrix by identifying the lateral edges of the convex data scatter p…

We propose a technique for making Convolutional Neural Network (CNN)-based models more transparent by visualizing input regions that are 'important' for predictions -- or visual explanations. Our approach, called Gradient-weighted Class Activation Mapping (Grad-CAM), uses class-specific gradient information to localize…

Lower bounds show many sampling algorithms need many gradient queries.

Supporting evidence for adaptive feature program across diverse models.

Enhanced visibility forecasts using CAMS data improve accuracy.

New Fourier transform method handles missing data and asynchronous observations.

Functional groups (FGs) are molecular substructures that are served as a foundation for analyzing and predicting chemical properties of molecules. Automatic discovery of FGs will impact various fields of research, including medicinal chemistry and material sciences, by reducing the amount of lab experiments required fo…

Dans les années 1940-1970, Alexandrov et l'"École de Leningrad" ont développé une théorie très riche des surfaces singulières. Il s'agit de surfaces topologiques, munie d'une métrique intrinsèque pour laquelle on peut définir une notion de courbure, qui est une mesure de Radon. Cette classe de surfaces a de bonnes prop…

The homology groups of a manifold are important topological invariants that provide an algebraic summary of the manifold. These groups contain rich topological information, for instance, about the connected components, holes, tunnels and sometimes the dimension of the manifold. In earlier work, we have considered the s…

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…

New complexity measure for interactive learning reduces regret to near-optimal levels.

Differential privacy formalises privacy-preserving mechanisms that provide access to a database. We pose the question of whether Bayesian inference itself can be used directly to provide private access to data, with no modification. The answer is affirmative: under certain conditions on the prior, sampling from the pos…

Consider a two-class clustering problem where we observe $X_i = \ell_i μ+ Z_i$, $Z_i \stackrel{iid}{\sim} N(0, I_p)$, $1 \leq i \leq n$. The feature vector $μ\in R^p$ is unknown but is presumably sparse. The class labels $\ell_i\in\{-1, 1\}$ are also unknown and the main interest is to estimate them. We are interested …

VRPG algorithm optimizes convex constraints with non-asymptotic guarantees.

Extends causal additive models to include higher-order interactions.

We inspect the BNSR-invariants $Σ^m(P_n)$ of the pure braid groups $P_n$, using Morse theory. The BNS-invariants $Σ^1(P_n)$ were previously computed by Koban, McCammond and Meier. We prove that for any $3\le m\le n$, the inclusion $Σ^{m-2}(P_n)\subseteq Σ^{m-3}(P_n)$ is proper, but $Σ^\infty(P_n)=Σ^{n-2}(P_n)$. We writ…

Locally private mechanisms' output divergence bounds derived.

Developable ruled surfaces generated by curvature axes of curves.

Develops high-probability minimax quantile bounds for statistical problems.

Deep neural features identify unique vehicles from dash-cam feeds.

Paper proposes methods to discover causal models with unobserved variables.

Floer theory connects dynamics on surfaces to their chain-level theory.

CAMS selects best pre-trained model for unlabeled data points.

Unified framework recovers and improves classical Brouwer homeomorphism results.

New method finds rare dense clusters in asymmetric binary perceptrons, resolving algorithmic hardness.

The paper finds infinitely many half-volume CMC hypersurfaces on generic or Ricci-positive manifolds.

We refine a Le and Murakami uniqueness theorem for the Kontsevich Integral in order to specify the relationship between the two (possibly equal) main universal link invariants: the Kontsevich Integral and the perturbative expression of the Chern-Simons theory. As a corollary, we prove that the Altschuler and Freidel an…

A new method is proposed to obtain the risk neutral probability of share prices without stochastic calculus and price modeling, via an embedding of the price return modeling problem in Le Cam's statistical experiments framework. Strategies-probabilities $P_{t_0,n}$ and $P_{T,n}$ are thus determined and used, respective…

Paper develops an online covariance estimator for nonsmooth stochastic approximation problems.

CNNs help diagnose diabetic retinopathy by localizing lesions.

The study finds minimal hypersurfaces in wedge-shaped manifolds with boundary.