Related papers: Numerical Analysis of Test Optimality
We investigate the proximal map for the weighted mean absolute error function. An algorithm for its efficient and vectorized evaluation is presented. As a demonstration, this algorithm is applied as part of a checkerboard algorithm to solve…
This paper investigates recently proposed approaches for defending against adversarial examples and evaluating adversarial robustness. We motivate 'adversarial risk' as an objective for achieving models robust to worst-case inputs. We then…
For many important problems the quantity of interest is an unknown function of the parameters, which is a random vector with known statistics. Since the dependence of the output on this random vector is unknown, the challenge is to identify…
Minimizing the number of patients exposed to potentially harmful drugs in early onco logical trials is a major concern during planning. Adaptive designs account for the inherent uncertainty about the true effect size by determining the…
We consider the problem of estimating the states of weakly coupled linear systems from sampled measurements. We assume that the total capacity available to the sensors to transmit their samples to a network manager in charge of the…
The present paper gives a statistical adventure towards exploring the average case complexity behavior of computer algorithms. Rather than following the traditional count based analytical (pen and paper) approach, we instead talk in terms…
We endeavour to estimate numerous multi-dimensional means of various probability distributions on a common space based on independent samples. Our approach involves forming estimators through convex combinations of empirical means derived…
The majority of machine learning methods can be regarded as the minimization of an unavailable risk function. To optimize the latter, given samples provided in a streaming fashion, we define a general stochastic Newton algorithm and its…
The classical binary hypothesis testing problem is revisited. We notice that when one of the hypotheses is composite, there is an inherent difficulty in defining an optimality criterion that is both informative and well-justified. For…
In optimization problems, the quality of a candidate solution can be characterized by the optimality gap. For most stochastic optimization problems, this gap must be statistically estimated. We show that for risk-averse problems, standard…
Matching a nonprobability sample to a probability sample is one strategy both for selecting the nonprobability units and for weighting them. This approach has been employed in the past to select subsamples of persons from a large panel of…
A new gradient-based adaptive sampling method is proposed for design of experiments applications which balances space filling, local refinement, and error minimization objectives while reducing reliance on delicate tuning parameters. High…
We consider nonadaptive probabilistic group testing in the linear regime, where each of n items is defective independently with probability p in (0,1), and p is a constant independent of n. We show that testing each item individually is…
We consider goodness-of-fit tests for uniformity of a multinomial distribution by means of tests based on a class of symmetric statistics, defined as the sum of some function of cell-frequencies. We are dealing with an asymptotic regime,…
Algorithms based on non-unitary evolution have attracted much interest for ground state preparation on quantum computers. One recently proposed method makes use of ancilla qubits and controlled unitary operators to implement weak…
We give a general unified method that can be used for $L_1$ {\em closeness testing} of a wide range of univariate structured distribution families. More specifically, we design a sample optimal and computationally efficient algorithm for…
The weighted average is by far the most popular approach to combining multiple forecasts of some future outcome. This paper shows that both for probability or real-valued forecasts, a non-trivial weighted average of different forecasts is…
Practical model building processes are often time-consuming because many different models must be trained and validated. In this paper, we introduce a novel algorithm that can be used for computing the lower and the upper bounds of model…
In the problem of composite hypothesis testing, identifying the potential uniformly most powerful (UMP) unbiased test is of great interest. Beyond typical hypothesis settings with exponential family, it is usually challenging to prove the…
Neural networks are becoming increasingly prevalent in software, and it is therefore important to be able to verify their behavior. Because verifying the correctness of neural networks is extremely challenging, it is common to focus on the…