Related papers: On Confidence Sequences for Bounded Random Process…
We study T. Cover's rebalancing option (Ordentlich and Cover 1998) under discrete hindsight optimization in continuous time. The payoff in question is equal to the final wealth that would have accrued to a $\$1$ deposit into the best of…
Consider betting against a sequence of data in $[0,1]$, where one is allowed to make any bet that is fair if the data have a conditional mean $m_0 \in (0,1)$. Cover's universal portfolio algorithm delivers a worst-case regret of $O(\ln n)$…
In most prediction and estimation situations, scientists consider various statistical models for the same problem, and naturally want to select amongst the best. Hansen et al. (2011) provide a powerful solution to this problem by the…
We revisit the classical problem of universal prediction of stochastic sequences with a finite time horizon $T$ known to the learner. The question we investigate is whether it is possible to derive vanishing regret bounds that hold with…
We develop a general framework for conducting inference on the mean of dependent random variables given constraints on their dependency graph. We establish the consistency of an oracle variance estimator of the mean when the dependency…
In this paper, we discuss the asymptotic behavior of the Upper Confidence Bound (UCB) algorithm in the context of multiarmed bandit problems and discuss its implication in downstream inferential tasks. While inferential tasks become…
In this paper, we propose a general method for testing composite hypotheses. Our idea is to use confidence limits to define stopping and decision rules. The requirements of operating characteristic function can be satisfied by adjusting the…
A confidence sequence (CS) is an anytime-valid sequential inference primitive which produces an adapted sequence of sets for a predictable parameter sequence with a time-uniform coverage guarantee. This work constructs a non-parametric…
In this paper, we consider the problem of guessing a sequence subject to a distortion constraint. Specifically, we assume the following game between Alice and Bob: Alice has a sequence $\bx$ of length $n$. Bob wishes to guess $\bx$, yet he…
In this paper, we propose new sequential estimation methods based on inclusion principle. The main idea is to reformulate the estimation problems as constructing sequential random intervals and use confidence sequences to control the…
We consider a statistical test whose p-value can only be approximated using Monte Carlo simulations. We are interested in deciding whether the p-value for an observed data set lies above or below a given threshold such as 5%. We want to…
We introduce a graceful approach to probabilistic inference called bounded conditioning. Bounded conditioning monotonically refines the bounds on posterior probabilities in a belief network with computation, and converges on final…
We consider universal inference in variance components models, focusing on settings where the parameter is near or at the boundary of the parameter set. Two cases, which are not handled by existing state-of-the-art methods, are of…
Game-theoretic upper expectations are joint (global) probability models that mathematically describe the behaviour of uncertain processes in terms of supermartingales; capital processes corresponding to available betting strategies.…
Gaussian Processes (GPs) are widely employed in control and learning because of their principled treatment of uncertainty. However, tracking uncertainty for iterative, multi-step predictions in general leads to an analytically intractable…
We propose confidence sequences -- sequences of confidence intervals which are valid uniformly over time -- for quantiles of any distribution over a complete, fully-ordered set, based on a stream of i.i.d. observations. We give methods both…
Motivated by problems of learning to rank long item sequences, we introduce a variant of the cascading bandit model that considers flexible length sequences with varying rewards and losses. We formulate two generative models for this…
A number of algorithms have been developed to solve probabilistic inference problems on belief networks. These algorithms can be divided into two main groups: exact techniques which exploit the conditional independence revealed when the…
The partial monitoring (PM) framework provides a theoretical formulation of sequential learning problems with incomplete feedback. On each round, a learning agent plays an action while the environment simultaneously chooses an outcome. The…
In business retention, churn prevention has always been a major concern. This work contributes to this domain by formalizing the problem of churn prediction in the context of online gambling as a binary classification task. We also propose…