Related papers: On Optimal Solutions to Compound Statistical Decis…
Optimization under uncertainty and risk is indispensable in many practical situations. Our paper addresses stability of optimization problems using composite risk functionals which are subjected to measure perturbations. Our main focus is…
One of the central issues in the hidden subgroup problem is to bound the sample complexity, i.e., the number of identical samples of coset states sufficient and necessary to solve the problem. In this paper, we present general bounds for…
A new method of deriving comparative statics information using generalized compensated derivatives is presented which yields constraint-free semidefiniteness results for any differentiable, constrained optimization problem. More generally,…
Randomized approximation algorithms for many #P-complete problems (such as the partition function of a Gibbs distribution, the volume of a convex body, the permanent of a $\{0,1\}$-matrix, and many others) reduce to creating random…
We derive asymptotically optimal statistical decision rules for discrete choice problems when payoffs depend on a partially-identified parameter $\theta$ and the decision maker can use a point-identified parameter $\mu$ to deduce…
We model the joint distribution of choice probabilities and decision times in binary choice tasks as the solution to a problem of optimal sequential sampling, where the agent is uncertain of the utility of each action and pays a constant…
The study of a machine learning problem is in many ways is difficult to separate from the study of the loss function being used. One avenue of inquiry has been to look at these loss functions in terms of their properties as scoring rules…
We study a fundamental stochastic selection problem involving $n$ independent random variables, each of which can be queried at some cost. Given a tolerance level $\delta$, the goal is to find a value that is $\delta$-approximately minimum…
We consider two related problems arising from a question of R. Graham on quasirandom phenomena in permutation patterns. A ``pattern'' in a permutation $\sigma$ is the order type of the restriction of $\sigma : [n] \to [n]$ to a subset $S…
We consider the problem of jointly testing multiple hypotheses and estimating a random parameter of the underlying distribution. This problem is investigated in a sequential setup under mild assumptions on the underlying random process. The…
We consider the sequential composite binary hypothesis testing problem in which one of the hypotheses is governed by a single distribution while the other is governed by a family of distributions whose parameters belong to a known set…
We study the problem of optimal subset selection from a set of correlated random variables. In particular, we consider the associated combinatorial optimization problem of maximizing the determinant of a symmetric positive definite matrix…
We prove several new tight distributed lower bounds for classic symmetry breaking graph problems. As a basic tool, we first provide a new insightful proof that any deterministic distributed algorithm that computes a $\Delta$-coloring on…
We present a new optimization method for the group selection problem in linear regression. In this problem, predictors are assumed to have a natural group structure and the goal is to select a small set of groups that best fits the…
Existing statistical approaches to natural language problems are very coarse approximations to the true complexity of language processing. As such, no single technique will be best for all problem instances. Many researchers are examining…
We consider the problem of sequential hypothesis testing by betting. For a general class of composite testing problems -- which include bounded mean testing, equal mean testing for bounded random tuples, and some key ingredients of…
Teaching how to derive minimax decision rules can be challenging because of the lack of examples that are simple enough to be used in the classroom. Motivated by this challenge, we provide a new example that illustrates the use of standard…
We present a framework for the theoretical analysis of ensembles of low-complexity empirical risk minimisers trained on independent random compressions of high-dimensional data. First we introduce a general distribution-dependent…
We consider combinatorial optimization problems defined over random ensembles, and study how solution cost increases when the optimal solution undergoes a small perturbation delta. For the minimum spanning tree, the increase in cost scales…
In "Recognizing the Maximum of a Sequence", Gilbert and Mosteller analyze a full information game where n measurements from an uniform distribution are drawn and a player (knowing n) must decide at each draw whether or not to choose that…