相关论文: On Sequence Prediction for Arbitrary Measures

A new notion of typicality for arbitrary probability measures on standard Borel spaces is proposed, which encompasses the classical notions of weak and strong typicality as special cases. Useful lemmas about strong typical sets, including…

In this paper, we study the classical problem of estimating the proportion of a finite population. First, we consider a fixed sample size method and derive an explicit sample size formula which ensures a mixed criterion of absolute and…

In the binary hypothesis testing problem, it is well known that sequentiality in taking samples eradicates the trade-off between two error exponents, yet implementing the optimal test requires the knowledge of the underlying distributions,…

We investigate the inverse problem of identifying a conditional probability measure in a measure-dependent dynamical system. We provide existence and well-posedness results and outline a discretization scheme for approximating a measure.…

This paper concerns instruction sequences that contain probabilistic instructions, i.e. instructions that are themselves probabilistic by nature. We propose several kinds of probabilistic instructions, provide an informal operational…

Estimating a constrained relation is a fundamental problem in machine learning. Special cases are classification (the problem of estimating a map from a set of to-be-classified elements to a set of labels), clustering (the problem of…

An important tool to quantify the likeness of two probability measures are f-divergences, which have seen widespread application in statistics and information theory. An example is the total variation, which plays an exceptional role among…

Nonprobability (convenience) samples are increasingly sought to stabilize estimations for one or more population variables of interest that are performed using a randomized survey (reference) sample by increasing the effective sample size.…

In this paper we derive variability measures for the conditional probability distributions of a pair of random variables, and we study its application in the inference of causal-effect relationships. We also study the combination of the…

Given a collection of computational models that all estimate values of the same natural process, we compare the performance of the average of the collection to the individual member whose estimates are nearest a given set of observations.…

In some particular cases we give criteria for morphic sequences to be almost periodic (=uniformly recurrent). Namely, we deal with fixed points of non-erasing morphisms and with automatic sequences. In both cases a polynomial-time algorithm…

A dependence measure for arbitrary type pairs of random variables is proposed and analyzed, which in the particular case where both random variables are continuous turns out to be a concordance measure. Also, a sample version of the…

Language modeling, a central task in natural language processing, involves estimating a probability distribution over strings. In most cases, the estimated distribution sums to 1 over all finite strings. However, in some pathological cases,…

We present local ensembles, a method for detecting underspecification -- when many possible predictors are consistent with the training data and model class -- at test time in a pre-trained model. Our method uses local second-order…

The problem of measurement in quantum mechanics is reanalyzed within a general, strictly probabilistic framework (without reduction postulate). Based on a novel comprehensive definition of measurement the natural emergence of objective…

Stern's diatomic sequence with its intrinsic repetition and refinement structure between consecutive powers of $2$ gives rise to a rather natural probability measure on the unit interval. We construct this measure and show that it is purely…

A person is given a numbered sequence of positions on a sheet of paper. The person is asked, "Which will be the next (or the next after that) position?" Everyone has an opinion as to how he or she would proceed. There are regular sequences…

We present a class of models that, via a simple construction, enables exact, incremental, non-parametric, polynomial-time, Bayesian inference of conditional measures. The approach relies upon creating a sequence of covers on the…

We consider the problem of deciding whether a given state preparation, i.e., a source of quantum states, is accurate, namely produces states close to a target one within a prescribed threshold. We show that, when multiple measurements need…

From behavioral sciences to biology to quantum mechanics, one encounters situations where (i) a system outputs several random variables in response to several inputs, (ii) for each of these responses only some of the inputs may "directly"…