Related papers: Exponential Stochastic Inequality
Generalization bounds which assess the difference between the true risk and the empirical risk, have been studied extensively. However, to obtain bounds, current techniques use strict assumptions such as a uniformly bounded or a Lipschitz…
Scalar inferences (SI) are a signature example of how humans interpret language based on unspoken alternatives. While empirical studies have demonstrated that human SI rates are highly variable -- both within instances of a single scale,…
For a set of binary response variables, conditional mean models characterize the expected value of a response variable given the others and are popularly applied in longitudinal and network data analyses. The quadratic exponential binary…
Statistical machine learning theory often tries to give generalization guarantees of machine learning models. Those models naturally underlie some fluctuation, as they are based on a data sample. If we were unlucky, and gathered a sample…
A large class of problems in sciences and engineering can be formulated as the general problem of constructing random intervals with pre-specified coverage probabilities for the mean. Wee propose a general approach for statistical inference…
In this brief paper we find computable exponential convergence rates for a large class of stochastically ordered Markov processes. We extend the result of Lund, Meyn, and Tweedie (1996), who found exponential convergence rates for…
We give improved constants for data dependent and variance sensitive confidence bounds, called empirical Bernstein bounds, and extend these inequalities to hold uniformly over classes of functionswhose growth function is polynomial in the…
Many practical machine learning tasks can be framed as Structured prediction problems, where several output variables are predicted and considered interdependent. Recent theoretical advances in structured prediction have focused on…
One of the defining properties of deep learning is that models are chosen to have many more parameters than available training data. In light of this capacity for overfitting, it is remarkable that simple algorithms like SGD reliably return…
We obtain non-uniform Edgeworth expansions for several classes of weakly dependent (non-stationary) sequences of random variables, including uniformly elliptic inhomogeneous Markov chains, random and time-varying (partially) hyperbolic or…
Unlike equilibrium statistical mechanics, with its well-established foundations, a similar widely-accepted framework for non-equilibrium statistical mechanics (NESM) remains elusive. Here, we review some of the many recent activities on…
The overarching goal of this paper is to derive excess risk bounds for learning from exp-concave loss functions in passive and sequential learning settings. Exp-concave loss functions encompass several fundamental problems in machine…
I propose a novel framework that integrates stochastic differential equations (SDEs) with deep generative models to improve uncertainty quantification in machine learning applications involving structured and temporal data. This approach,…
Linear Autoencoders (LAEs) have shown strong performance in state-of-the-art recommender systems. However, this success remains largely empirical, with limited theoretical understanding. In this paper, we investigate the generalizability --…
Extreme value functionals of stochastic processes are inverse functionals of the first passage time -- a connection that renders their probability distribution functions equivalent. Here, we deepen this link and establish a framework for…
This thesis is devoted to the study of extreme value statistics in stochastic processes and their applications. In the first part, we obtain exact analytical results on the extreme value statistics of both discrete-time and continuous-time…
In real-world applications, the distribution of the data, and our goals, evolve over time. The prevailing theoretical framework for studying machine learning, namely probably approximately correct (PAC) learning, largely ignores time. As a…
In this paper we show irreducibility and the strong Feller property for transition probabilities of stochastic differential equations with jumps and monotone coefficients. Thus, exponential ergodicity and the spectral gap for the…
Positivity, the assumption that every unique combination of confounding variables that occurs in a population has a non-zero probability of an action, can be further delineated as deterministic positivity and stochastic positivity. Here, we…
A Bayesian non-parametric framework for studying time-to-event data is proposed, where the prior distribution is allowed to depend on an additional random source, and may update with the sample size. Such scenarios are natural, for…