Related papers: Optimality of Universal Bayesian Sequence Predicti…
We consider the Bayesian optimal filtering problem: i.e. estimating some conditional statistics of a latent time-series signal from an observation sequence. Classical approaches often rely on the use of assumed or estimated transition and…
In the online prediction framework, we use generalized entropy of to study the loss rate of predictors when outcomes are drawn according to stationary ergodic distributions over the binary alphabet. We show that the notion of generalized…
Motivated by the evident success of context-tree based methods in lossless data compression, we explore, in this paper, methods of the same spirit in universal prediction of individual sequences. By context-tree prediction, we refer to a…
A Bayesian network is a widely used probabilistic graphical model with applications in knowledge discovery and prediction. Learning a Bayesian network (BN) from data can be cast as an optimization problem using the well-known…
The main purpose of this article is to prove that, under certain assumptions in a linear prediction setting, optimal methods based upon model reduction and even an optimal predictor can be provided. The optimality is formulated in terms of…
We establish rates of convergences in time series forecasting using the statistical learning approach based on oracle inequalities. A series of papers extends the oracle inequalities obtained for iid observations to time series under weak…
We extend stochastic network optimization theory to treat networks with arbitrary sample paths for arrivals, channels, and mobility. The network can experience unexpected link or node failures, traffic bursts, and topology changes, and…
Forecasting revenues by aggregating analyst forecasts is a fundamental problem in financial research and practice. A key objective in this context is to improve the accuracy of the forecast by optimizing two performance metrics: the hit…
Sequential probability assignment and universal compression go hand in hand. We propose sequential probability assignment for non-binary (and large alphabet) sequences with empirical distributions whose parameters are known to be bounded…
Solomonoff unified Occam's razor and Epicurus' principle of multiple explanations to one elegant, formal, universal theory of inductive inference, which initiated the field of algorithmic information theory. His central result is that the…
The Bayesian framework is a well-studied and successful framework for inductive reasoning, which includes hypothesis testing and confirmation, parameter estimation, sequence prediction, classification, and regression. But standard…
We consider the problem of jointly testing multiple hypotheses and estimating a random parameter of the underlying distribution. This problem is investigated in a sequential setup under mild assumptions on the underlying random process. The…
In this article, a general problem of sequential statistical inference for general discrete-time stochastic processes is considered. The problem is to minimize an average sample number given that Bayesian risk due to incorrect decision does…
We introduce a new concept of approximation applicable to decision problems and functions, inspired by Bayesian probability. From the perspective of a Bayesian reasoner with limited computational resources, the answer to a problem that…
Consider a finite set of sources, each producing i.i.d. observations that follow a unique probability distribution on a finite alphabet. We study the problem of matching a finite set of observed sequences to the set of sources under the…
We give some results relating asymptotic characterisations of maximum entropy probability measures to characterisations of Bayes optimal classifiers. Our main theorems show that maximum entropy is a universally Bayes optimal decision rule…
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 study the properties of the Minimum Description Length principle for sequence prediction, considering a two-part MDL estimator which is chosen from a countable class of models. This applies in particular to the important case of…
A sequence $x_1,\dots,x_n,\dots$ of discrete-valued observations is generated according to some unknown probabilistic law (measure) $\mu$. After observing each outcome, one is required to give conditional probabilities of the next…
In the framework of prediction of individual sequences, sequential prediction methods are to be constructed that perform nearly as well as the best expert from a given class. We consider prediction strategies that compete with the class of…