arXiv research

Data processing inequalities link Fisher information to local differential privacy constraints.

The paper improves count data regression models for overdispersed data.

Study introduces new Bernstein inequalities for dependent data in Hilbert spaces.

Paper develops a new inequality for non-causal machine learning.

New statistical inference method for high-dimensional Hawkes processes.

Develops inequalities for high-dimensional linear processes with dependent innovations.

Unified framework for deriving generalization bounds in supervised learning.

The data processing inequality doesn't always hold in practice, showing benefits in low-level tasks.

Study hypothesis testing under quantized samples with communication constraints, achieving near-optimal sample complexity.

We consider the Harnack inequality for harmonic functions with respect to three types of infinite dimensional operators. For the infinite dimensional Laplacian, we show no Harnack inequality is possible. We also show that the Harnack inequality fails for a large class of Ornstein-Uhlenbeck processes, although functions…

From concentration inequalities for the suprema of Gaussian or Rademacher processes an inequality is derived. It is applied to sharpen existing and to derive novel bounds on the empirical Rademacher complexities of unit balls in various norms appearing in the context of structured sparsity and multitask dictionary lear…

Paper sets fundamental limits for distributed covariance estimation with constrained communication.

The paper analyzes convergence rates of Langevin dynamics and Proximal Sampler using $Φ$-divergence.

In this short note, we will strengthen the classic Doob's $L^p$ inequality for sub-martingale processes. Because this inequality is of fundamental importance to the theory of stochastic process, we believe this generalization will find many interesting applications.

The paper improves machine learning for heavy-tailed panel data.

Study of diffusion annealed Langevin dynamics for generative models.

The paper proves concentration inequalities for diffusion processes.

Gaussian process (GP) modulated Cox processes are widely used to model point patterns. Existing approaches require a mapping (link function) between the unconstrained GP and the positive intensity function. This commonly yields solutions that do not have a closed form or that are restricted to specific covariance funct…

New approach shows data memorization trade-offs in large models.

New measures generalize existing ones, linking information and risk.

Improved analysis of UCRL2 with empirical Bernstein inequality reduces exploration-exploitation regret.

Introducing inequality constraints in Gaussian process (GP) models can lead to more realistic uncertainties in learning a great variety of real-world problems. We consider the finite-dimensional Gaussian approach from Maatouk and Bay (2017) which can satisfy inequality conditions everywhere (either boundedness, monoton…

We study the tradeoff between the statistical error and communication cost of distributed statistical estimation problems in high dimensions. In the distributed sparse Gaussian mean estimation problem, each of the $m$ machines receives $n$ data points from a $d$-dimensional Gaussian distribution with unknown mean $θ$ w…

Paper improves risk bound for MTL with graph-dependent data.

Adding inequality constraints (e.g. boundedness, monotonicity, convexity) into Gaussian processes (GPs) can lead to more realistic stochastic emulators. Due to the truncated Gaussianity of the posterior, its distribution has to be approximated. In this work, we consider Monte Carlo (MC) and Markov Chain Monte Carlo (MC…

New sparse Gaussian process method tackles unconstrained regression problems.

This paper investigates the supervised learning problem with observations drawn from certain general stationary stochastic processes. Here by \emph{general}, we mean that many stationary stochastic processes can be included. We show that when the stochastic processes satisfy a generalized Bernstein-type inequality, a u…

Quantifies fractional isoperimetric inequality with strong control over boundary oscillation.

The paper proves concentration inequalities for two-sample rank processes and applies them to ranking performance criteria.

In this paper, we propose a novel framework to analyze the theoretical properties of the learning process for a representative type of domain adaptation, which combines data from multiple sources and one target (or briefly called representative domain adaptation). In particular, we use the integral probability metric t…

Let $({\M}, g(t))$ be a Kähler Ricci flow with positive first Chern class. We prove a uniform isoperimetric inequality for all time. In the process we also prove a Cheng-Yau type log gradient bound for positive harmonic functions on $({\M}, g(t))$, and a Poincaré inequality without assuming the Ricci curvature is bound…

We study a sparse negative binomial regression (NBR) for count data by showing the non-asymptotic advantages of using the elastic-net estimator. Two types of oracle inequalities are derived for the NBR's elastic-net estimates by using the Compatibility Factor Condition and the Stabil Condition. The second type of oracl…

Quantum states can be learned efficiently using gentle measurements.

The paper proves a diastolic inequality linking surface area and loop length.

Paper outlines a new mathematical language for experiments.

Study improves self-normalized bounds for vector-valued processes beyond sub-Gaussianity.

Microstructure of market dynamics is studied through analysis of tick price data. Linear trend is introduced as a tool for such analysis. Trend arbitrage inequality is developed and tested. The inequality sets limiting relationship between trend, bid-ask spread, market reaction and average update frequency of price inf…

We prove structure theorems for complete manifolds satisfying both the Ricci curvature lower bound and the weighted Poincaré inequality. In the process, a sharp decay estimate for the minimal positive Green's function is obtained. This estimate only depends on the weight function of the Poincaré inequality, and yields …

Develops robust MDPs for unknown disturbances with performance guarantees.

Probability distributions of money, income, and energy consumption per capita are studied for ensembles of economic agents. The principle of entropy maximization for partitioning of a limited resource gives exponential distributions for the investigated variables. A non-equilibrium difference of money temperatures betw…

New approach to concentration inequalities for unbounded state space dynamical systems.

We improve bounds for stochastic processes, especially those with heavy tails.

Extended Ville's inequality for nonintegrable supermartingales.

We investigate properties of estimators obtained by minimization of U-processes with the Lasso penalty in high-dimensional settings. Our attention is focused on the ranking problem that is popular in machine learning. It is related to guessing the ordering between objects on the basis of their observed predictors. We p…

New method detects changes in high-dimensional Markov processes without explicit likelihood evaluation.

We prove a uniform Sobolev inequality along the Sasaki-Ricci flow. In the process, we develop the theory of basic Lebesgue and Sobolev function spaces, and prove some general results about the decomposition of the heat kernel for a class of elliptic operators on a Sasaki manifold.

Study non-Gaussian measures' concentration properties in metric spaces.

Paper analyzes statistical efficiency of TD learning in Hilbert spaces with Freedman's inequality.