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.

Stochastic approximation proves asymptotic normality for non-smooth problems.

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 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 …

"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.

New framework resolves central limit behavior in differential privacy.

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…

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

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

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

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 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…

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…

We study the volatility functional inference by Fourier transforms. This spectral framework is advantageous in that it harnesses the power of harmonic analysis to handle missing data and asynchronous observations without any artificial time alignment nor data imputation. Under conditions, this spectral approach is cons…

Unified diffusive bounds for non-linear parabolic equations.

Supporting evidence for adaptive feature program across diverse models.

Enhanced visibility forecasts using CAMS data improve accuracy.

We present a new short proof of the explicit formula for the group of links (and also link maps) in the 'quadruple point free' dimension. Denote by $L^m_{p,q}$ (respectively, $C^{m-p}_p$) the group of smooth embeddings $S^p\sqcup S^q\to S^m$ (respectively, $S^p\to S^m$) up to smooth isotopy. Denote by $LM^m_{p,q}$ the …

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…

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…

Nous montrons que les équations du repère mobile des surfaces de Bonnet conduisent à une paire de Lax matricielle isomonodromique d'ordre deux pour la sixième équation de Painlevé. We show that the moving frame equations of Bonnet surfaces can be extrapolated to a second order, isomonodromic matrix Lax pair of the sixt…

New proof for rotationally symmetric gradient Ricci solitons in 2-4 dimensions.

Let $(M,g(t))$, $0\le t\le T$, be a n-dimensional complete noncompact manifold, $n\ge 2$, with bounded curvatures and metric $g(t)$ evolving by the Ricci flow $\frac{\partial g_{ij}}{\partial t}=-2R_{ij}$. We will extend the result of L. Ma and Y. Yang and prove a local gradient estimate for positive solutions of the n…

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…

Establishes a concavity property for positive Hessian quotient operators.

Compactness of metrics with higher-order constant Q-curvature on manifolds.

VRPG algorithm optimizes convex constraints with non-asymptotic guarantees.

Let $(M,g(t))$, $0\le t\le T$, $\partial M\neφ$, be a compact $n$-dimensional manifold, $n\ge 2$, with metric $g(t)$ evolving by the Ricci flow such that the second fundamental form of $\partial M$ with respect to the unit outward normal of $\partial M$ is uniformly bounded below on $\partial M\times [0,T]$. We will pr…

Extends causal additive models to include higher-order interactions.

Locally private mechanisms' output divergence bounds derived.

This paper deals with finding an $n$-dimensional solution $x$ to a system of quadratic equations of the form $y_i=|\langle{a}_i,x\rangle|^2$ for $1\le i \le m$, which is also known as phase retrieval and is NP-hard in general. We put forth a novel procedure for minimizing the amplitude-based least-squares empirical los…

We study the asymptotic Dirichlet problem for the minimal graph equation on a Cartan-Hadamard manifold $M$ whose radial sectional curvatures outside a compact set satisfy an upper bound $K(P)\le - \frac{φ(φ-1)}{r(x)^2}$ and a pointwise pinching condition $|K(P)|\le C_K|K(P')|$ for some constants $φ>1$ and $C_K\ge 1…

New findings on Helmholtz equation solutions show exponential growth in constant for three ball inequality.

Method shows existence of conformal metrics with constant $Q$-curvature on manifolds.

Develops high-probability minimax quantile bounds for statistical problems.

Lower bounds show many sampling algorithms need many gradient queries.

Study on blow-up behavior of sign-changing solutions for Yamabe equation.

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

Paper proposes methods to discover causal models with unobserved variables.

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

The paper analyzes McKean-Vlasov equations with hitting times, proving global solvability.

Let n>2, $0<m\le (n-2)/n$, p>\max(1,(1-m)n/2), and $0\le u_0\in L_{loc}^p(R^n)$ satisfy $\liminf_{R\to\infty}R^{-n+\frac{2}{1-m}}\int_{|x|\le R}u_0\,dx=\infty$. We prove the existence of unique global classical solution of $u_t=\frac{n-1}{m}Δu^m$, u>0, in $R^n\times (0,\infty)$, u(x,0)=u_0(x) in $\R^n$. If in addition …