Related papers: A Unified Study on Sequentiality in Universal Clas…
The achievable error-exponent pairs for the type I and type II errors are characterized in a hypothesis testing setup where the observation consists of independent and identically distributed samples from either a known joint probability…
Linear models are foundational tools in statistics and ubiquitous across the applied sciences. However, conventional statistical inference -- such as $t$-tests and $F$-tests -- are only valid at fixed sample sizes, making them unsuitable…
In group sequential designs, where several data looks are conducted for early stopping, we generally assume the vector of test statistics from the sequential analyses follows (at least approximately or asymptotially) a multivariate normal…
This survey is focused on certain sequential decision-making problems that involve optimizing over probability functions. We discuss the relevance of these problems for learning and control. The survey is organized around a framework that…
A novel method for sequential outlier detection in non-stationary time series is proposed. The method tests the null hypothesis of ``no outlier'' at each time point, addressing the multiple testing problem by bounding the error probability…
While many statistical procedures rely on a fixed sample size, sequential methods allow a decision-maker to adapt the sample size to achieve a given precision. In this way, sequential tests reduce the average number of observations required…
Coding and testing schemes for binary hypothesis testing over noisy networks are proposed and their corresponding type-II error exponents are derived. When communication is over a discrete memoryless channel (DMC), our scheme combines…
The problem of sequential change diagnosis is considered, where observations are obtained on-line, an abrupt change occurs in their distribution, and the goal is to quickly detect the change and accurately identify the post-change…
We generalize standard credal set models for imprecise probabilities to include higher order credal sets -- confidences about confidences. In doing so, we specify how an agent's higher order confidences (credal sets) update upon observing…
We consider sequential hypothesis testing between two quantum states using adaptive and non-adaptive strategies. In this setting, samples of an unknown state are requested sequentially and a decision to either continue or to accept one of…
We consider the problem of sensor selection for time-optimal detection of a hypothesis. We consider a group of sensors transmitting their observations to a fusion center. The fusion center considers the output of only one randomly chosen…
In the uniformity testing task, an algorithm is provided with samples from an unknown probability distribution over a (known) finite domain, and must decide whether it is the uniform distribution, or, alternatively, if its total variation…
Dedicated to the memory of Professor Tze Leung Lai, this paper introduces three multi-hypothesis sequential tests. These tests are derived from one-sided versions of the sequential probability ratio test and its modifications. They are…
Let $X_1,X_2,..., X_n,...$ be a stochastic process with independent values whose distribution $P_\theta$ depends on an unknown parameter $\theta$, $\theta\in\Theta$, where $\Theta$ is an open subset of the real line. The problem of testing…
In this work, we give a novel general approach for distribution testing. We describe two techniques: our first technique gives sample-optimal testers, while our second technique gives matching sample lower bounds. As a consequence, we…
In many applications, accurate class probability estimates are required, but many types of models produce poor quality probability estimates despite achieving acceptable classification accuracy. Even though probability calibration has been…
The trade-off between the two types of errors in binary state discrimination may be quantified in the asymptotics by various error exponents. In the case of simple i.i.d. hypotheses, each of these exponents is equal to a divergence…
Under some mild Markov assumptions it is shown that the problem of designing optimal sequential tests for two simple hypotheses can be formulated as a linear program. The result is derived by investigating the Lagrangian dual of the…
We present an integrated prediction-optimization (PredOpt) framework to efficiently solve sequential decision-making problems by predicting the values of binary decision variables in an optimal solution. We address the key issues of…
The asymptotically optimal hypothesis testing problem with the general sources as the null and alternative hypotheses is studied under exponential-type error constraints on the first kind of error probability. Our fundamental philosophy in…