相关论文: On Concentration and Revisited Large Deviations An…
Experiments often yield non-identically distributed data for statistical analysis. Tests of hypothesis under such set-ups are generally performed using the likelihood ratio test, which is non-robust with respect to outliers and model…
In statistical analysis, measuring a score of predictive performance is an important task. In many scientific fields, appropriate scores were tailored to tackle the problems at hand. A proper score is a popular tool to obtain statistically…
In many contemporary statistical and machine learning methods, one needs to optimize an objective function that depends on the discrepancy between two probability distributions. The discrepancy can be referred to as a metric for…
The homotopy analysis method is studied in the present paper. The question of convergence of the homotopy analysis method is resolved. It is proven that under a special constraint the homotopy analysis method does converge to the exact…
The paper is concerned with a free boundary problem generated by the biharmonic operator and an obstacle. The main goal is to deduce a fully guaranteed upper bound of the difference between the exact minimizer u and any function…
This paper deals with the optimization of Bolza problem with a system of convex and nonconvex, discrete and differential state variable inequality constraints of second order by deriving necessary and sufficient conditions for optimality.…
We show sharpened forms of the concentration of measure phenomenon centered at first order stochastic expansions. The bound are based on second order difference operators and second order derivatives. Applications to functions on the…
We apply duality theory to discretized convex minimization problems to obtain computable guaranteed upper bounds for the distance of given discrete functions and the exact discrete minimizer. Furthermore, we show that the discrete duality…
In the present paper we shall study a variational problem relating the weighted Hardy inequalities with sharp missing terms. As weights we treat non-doubling functions of the distance to the boundary of bounded domain.
The notion of expectiles, originally introduced in the context of testing for homoscedasticity and conditional symmetry of the error distribution in linear regression, induces a law-invariant, coherent and elicitable risk measure that has…
The method to derive uniform bounds with Gaussian and Rademacher complexities is extended to the case where the sample average is replaced by a nonlinear statistic. Tight bounds are obtained for U-statistics, smoothened L-statistics and…
This paper provides an overview of results and concepts in minimax robust hypothesis testing for two and multiple hypotheses. It starts with an introduction to the subject, highlighting its connection to other areas of robust statistics and…
This paper is devoted to stability analysis of discrete-time delay systems based on a set of Lyapunov-Krasovskii functionals. New multiple summation inequalities are derived that involve the famous discrete Jensen's and Wirtinger's…
The problem of guessing a random string is revisited. A close relation between guessing and compression is first established. Then it is shown that if the sequence of distributions of the information spectrum satisfies the large deviation…
We study a one-dimensional exclusion process with a fixed jump length $I \ge 1$ in which a particle may advance or retreat $I$ sites provided all intermediate sites are vacant, with hopping rates of Arrhenius type depending on the local…
The celebrated Heinz inequality asserts that $ 2|||A^{1/2}XB^{1/2}|||\leq |||A^{\nu}XB^{1-\nu}+A^{1-\nu}XB^{\nu}|||\leq |||AX+XB|||$ for $X \in \mathbb{B}(\mathscr{H})$, $A,B\in \+$, every unitarily invariant norm $|||\cdot|||$ and $\nu \in…
Concentration inequalities, a major tool in probability theory, quantify how much a random variable deviates from a certain quantity. This paper proposes a systematic convex optimization approach to studying and generating concentration…
We propose a new Bayesian approach to generalize the federated Alternating Direction Method of Multipliers (ADMM). We show that the solutions of variational-Bayesian (VB) objectives are associated with a duality structure that not only…
We study adversarial binary hypothesis testing under memory constraints. The test is a time-invariant randomized finite state machine (FSM) with S states. Associated with each hypothesis is a set of distributions. Given the hypothesis, the…
In this paper, we further develop the approach, originating in [GJN], to "computation-friendly" hypothesis testing via Convex Programming. Most of the existing results on hypothesis testing aim to quantify in a closed analytic form…