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We consider the quickest change detection problem where both the parameters of pre- and post- change distributions are unknown, which prevents the use of classical simple hypothesis testing. Without additional assumptions, optimal solutions…

We consider semiparametric moment condition models invariant to transformation groups. The parameter of interest is estimated by minimum empirical divergence approach, introduced by Broniatowski and Keziou (2012). It is shown that the…

Modeled along the truncated approach in Panigrahi (2016), selection-adjusted inference in a Bayesian regime is based on a selective posterior. Such a posterior is determined together by a generative model imposed on data and the selection…

Error bounds based on worst likely assignments use permutation tests to validate classifiers. Worst likely assignments can produce effective bounds even for data sets with 100 or fewer training examples. This paper introduces a statistic…

We consider the minimum error entropy (MEE) criterion and an empirical risk minimization learning algorithm in a regression setting. A learning theory approach is presented for this MEE algorithm and explicit error bounds are provided in…

For normal canonical models, and more generally a vast array of general spherically symmetric location-scale models with a residual vector, we consider estimating the (univariate) location parameter when it is lower bounded. We provide…

During recent years the interest of optimization and machine learning communities in high-probability convergence of stochastic optimization methods has been growing. One of the main reasons for this is that high-probability complexity…

We analyze the best achievable performance of Bayesian learning under generative models by defining and upper-bounding the minimum excess risk (MER): the gap between the minimum expected loss attainable by learning from data and the minimum…

Quantum hypothesis testing is an important tool for quantum information processing. Two main strategies have been widely adopted: in a minimum error discrimination strategy, the average error probability is minimized; while in an…

Considering the problem of risk-sensitive parameter estimation, we propose a fairly wide family of lower bounds on the exponential moments of the quadratic error, both in the Bayesian and the non--Bayesian regime. This family of bounds,…

In numerous applications, surrogate models are used as a replacement for accurate parameter-to-observable mappings when solving large-scale inverse problems governed by partial differential equations (PDEs). The surrogate model may be a…

This study proposes the General Bayes framework for policy learning. We consider decision problems in which a decision-maker chooses an action from an action set to maximize its expected welfare. Typical examples include treatment choice…

We present a new uncertainty principle for risk-aware statistical estimation, effectively quantifying the inherent trade-off between mean squared error ($\mse$) and risk, the latter measured by the associated average predictive squared…

In this correspondence, we introduce a minimax regret criteria to the least squares problems with bounded data uncertainties and solve it using semi-definite programming. We investigate a robust minimax least squares approach that minimizes…

In machine learning, Domain Adaptation (DA) arises when the distribution gen- erating the test (target) data differs from the one generating the learning (source) data. It is well known that DA is an hard task even under strong assumptions,…

When a parameter of interest is defined to be a nondifferentiable transform of a regular parameter, the parameter does not have an influence function, rendering the existing theory of semiparametric efficient estimation inapplicable.…

We formulate, and present a numerical method for solving, an inverse problem for inferring parameters of a deterministic model from stochastic observational data (quantities of interest). The solution, given as a probability measure, is…

Most bandit algorithm designs are purely theoretical. Therefore, they have strong regret guarantees, but also are often too conservative in practice. In this work, we pioneer the idea of algorithm design by minimizing the empirical Bayes…

The Bayesian approach to machine learning amounts to computing posterior distributions of random variables from a probabilistic model of how the variables are related (that is, a prior distribution) and a set of observations of variables.…

We develop a framework for the operationalization of models and parameters by combining de Finetti's representation theorem with a conditional form of Sanov's theorem. This synthesis, the tilted de Finetti theorem, shows that conditioning…