Related papers: Statistical estimation requires unbounded memory
The paper considers estimates for some sums and products of functions of prime numbers. Several assertions on this topic have been proven. We also study extremal estimates for strongly additive and strongly multiplicative arithmetic…
Upper semicontinuous (usc) functions arise in the analysis of maximization problems, distributionally robust optimization, and function identification, which includes many problems of nonparametric statistics. We establish that every usc…
Estimation of mean and covariance functions is fundamental for functional data analysis. While this topic has been studied extensively in the literature, a key assumption is that there are enough data in the domain of interest to estimate…
In this paper we consider the problem of uniformity testing with limited memory. We observe a sequence of independent identically distributed random variables drawn from a distribution $p$ over $[n]$, which is either uniform or is…
Several recent works in communication systems have proposed to leverage the power of neural networks in the design of encoders and decoders. In this approach, these blocks can be tailored to maximize the transmission rate based on…
In this article, we construct semiparametrically efficient estimators of linear functionals of a probability measure in the presence of side information using an easy empirical likelihood approach. We use estimated constraint functions and…
We begin by introducing a class of conditional density estimators based on local polynomial techniques. The estimators are boundary adaptive and easy to implement. We then study the (pointwise and) uniform statistical properties of the…
We consider bipartitions of one-dimensional extended systems whose probability distribution functions describe stationary states of stochastic models. We define estimators of the shared information between the two subsystems. If the…
We investigate the modeling and the numerical solution of machine learning problems with prediction functions which are linear combinations of elements of a possibly infinite-dimensional dictionary. We propose a novel flexible composite…
A collaborative distributed binary decision problem is considered. Two statisticians are required to declare the correct probability measure of two jointly distributed memoryless process, denoted by $X^n=(X_1,\dots,X_n)$ and…
Measurements can be viewed as interactions between a measured system and a pointer system that imprint information about the system on the pointer. For so-called unbiased interactions, the measurement statistics--the information…
Using appropriate notation systems for proofs, cut-reduction can often be rendered feasible on these notations, and explicit bounds can be given. Developing a suitable notation system for Bounded Arithmetic, and applying these bounds, all…
The problem of extracting as much information as possible from a sequence of observations of a stationary stochastic process $X_0,X_1,...X_n$ has been considered by many authors from different points of view. It has long been known through…
We investigate learning collections of languages from texts by an inductive inference machine with access to the current datum and a bounded memory in form of states. Such a bounded memory states (BMS) learner is considered successful in…
An important step in the Markov reward approach to error bounds on stationary performance measures of Markov chains is to bound the bias terms. Affine functions have been successfully used for these bounds for various models, but there are…
We provide a variable metric stochastic approximation theory. In doing so, we provide a convergence theory for a large class of online variable metric methods including the recently introduced online versions of the BFGS algorithm and its…
It is known that 2-state binary and 3-state unary probabilistic finite automata and 2-state unary quantum finite automata recognize uncountably many languages with cutpoints. These results have been obtained by associating each recognized…
As models of cognition grow in complexity and number of parameters, Bayesian inference with standard methods can become intractable, especially when the data-generating model is of unknown analytic form. Recent advances in simulation-based…
We deal with the problem of optimal estimation of the linear functionals constructed from unobserved values of a continuous time stochastic process with periodically correlated increments based on past observations of this process. To solve…
We present general principles for the design and analysis of unbiased Monte Carlo estimators in a wide range of settings. Our estimators posses finite work-normalized variance under mild regularity conditions. We apply our estimators to…