Related papers: Deterministic Finite-Memory Bias Estimation

For long-memory time series, inference based on resampling is of crucial importance, since the asymptotic distribution can often be non-Gaussian and is difficult to determine statistically. However due to the strong dependence, establishing…

We consider the problem of identifying parameters of a particular class of Markov chains, called Bernoulli Autoregressive (BAR) processes. The structure of any BAR model is encoded by a directed graph. Incoming edges to a node in the graph…

Freidlin-Wentzell theory of large deviations can be used to compute the likelihood of extreme or rare events in stochastic dynamical systems via the solution of an optimization problem. The approach gives exponential estimates that often…

Any repeated use of a fixed experimental instrument is subject to memory effects. We design an estimation method uncovering the details of the underlying interaction between the system and the internal memory without having any experimental…

Suppose that i.i.d. random variables $X_{1}, X_{2}, \ldots$ are chosen uniformly from $[0,1]$, and let $f: [0,1] \rightarrow [0,1]$ be an increasing bijection. Define $\mu_{f}$ to be the expected value of $f(X_{i})$ for each $i$. Define the…

We consider linear two-time-scale stochastic approximation algorithms driven by martingale noise. Recent applications in machine learning motivate the need to understand finite-time error rates, but conventional stochastic approximation…

We address the self-stabilizing bit-dissemination problem, designed to capture the challenges of spreading information and reaching consensus among entities with minimal cognitive and communication capacities. Specifically, a group of $n$…

Given a random sample from a distribution with density function that depends on an unknown parameter $\theta$, we are interested in accurately estimating the true parametric density function at a future observation from the same…

High-dimensional models often have a large memory footprint and must be quantized after training before being deployed on resource-constrained edge devices for inference tasks. In this work, we develop an information-theoretic framework for…

Debiased machine learning (DML) offers an attractive way to estimate treatment effects in observational settings, where identification of causal parameters requires a conditional independence or unconfoundedness assumption, since it allows…

We consider a high-dimensional mean estimation problem over a binary hidden Markov model, which illuminates the interplay between memory in data, sample size, dimension, and signal strength in statistical inference. In this model, an…

We develop a stochastic approximation-type algorithm to solve finite state/action, infinite-horizon, risk-aware Markov decision processes. Our algorithm has two loops. The inner loop computes the risk by solving a stochastic saddle-point…

Two-time-scale Stochastic Approximation (SA) is an iterative algorithm with applications in reinforcement learning and optimization. Prior finite time analysis of such algorithms has focused on fixed point iterations with mappings…

The MDL two-part coding $ \textit{index of resolvability} $ provides a finite-sample upper bound on the statistical risk of penalized likelihood estimators over countable models. However, the bound does not apply to unpenalized maximum…

Variational inference methods for latent variable statistical models have gained popularity because they are relatively fast, can handle large data sets, and have deterministic convergence guarantees. However, in practice it is unclear…

We consider a one dimensional sub-ballistic random walk evolving in a parametric i.i.d. random environment. We study the asymptotic properties of the maximum likelihood estimator (MLE) of the parameter based on a single observation of the…

We study the local limit theorem for weighted sums of Bernoulli variables. We show on examples that this is an important question in the general theory of the local limit theorem, and which turns up to be not well explored. The examples we…

As sequential learning algorithms are increasingly applied to real life, ensuring data privacy while maintaining their utilities emerges as a timely question. In this context, regret minimisation in stochastic bandits under…

The uncertainty principle is a fundamental principle in quantum physics. It implies that the measurement outcomes of two incompatible observables can not be predicted simultaneously. In quantum information theory, this principle can be…

We address the problem of policy evaluation in discounted Markov decision processes, and provide instance-dependent guarantees on the $\ell_\infty$-error under a generative model. We establish both asymptotic and non-asymptotic versions of…