Related papers: A Selection Premium Decomposition for the Expected…

Feature selection by maximizing high-order mutual information between the selected feature vector and a target variable is the gold standard in terms of selecting the best subset of relevant features that maximizes the performance of…

We derive P(M,t_m), the joint probability density of the maximum M and the time t_m at which this maximum is achieved for a class of constrained Brownian motions. In particular, we provide explicit results for excursions, meanders and…

We review the cumulant decomposition (a way of decomposing the expectation of a product of random variables (e.g. $\mathbb{E}[XYZ]$) into a sum of terms corresponding to partitions of these variables.) and the Wick decomposition (a way of…

The problem of making sequential decisions in unknown probabilistic environments is studied. In cycle $t$ action $y_t$ results in perception $x_t$ and reward $r_t$, where all quantities in general may depend on the complete history. The…

In variable selection, most existing screening methods focus on marginal effects and ignore dependence between covariates. To improve the performance of selection, we incorporate pairwise effects in covariates for screening and…

Penalization of the likelihood by Jeffreys' invariant prior, or by a positive power thereof, is shown to produce finite-valued maximum penalized likelihood estimates in a broad class of binomial generalized linear models. The class of…

We address the fundamental problem of selection under uncertainty by modeling it from the perspective of Bayesian persuasion. In our model, a decision maker with imperfect information always selects the option with the highest expected…

A random walk with counterbalanced steps is a process of partial sums $\check S(n)=\check X_1+ \cdots + \check X_n$ whose steps $\check X_n$ are given recursively as follows. For each $n\geq 2$, with a fixed probability $p$, $\check X_n$ is…

Win statistics, including the win ratio, net benefit, and win odds, summarize treatment effects on hierarchical composite endpoints by sequentially comparing patient pairs on component outcomes ordered by clinical importance, proceeding to…

Consider a random walk $S_i= \xi_1+\ldots+\xi_i$, $i\in\mathbb N$, whose increments $\xi_1,\xi_2,\ldots$ are independent identically distributed random vectors in $\mathbb R^d$ such that $\xi_1$ has the same law as $-\xi_1$ and $\mathbb…

Let $X$ be the constrained random walk on $\mathbb{Z}_+^d$ $d >2$, having increments $e_1$, $-e_i+e_{i+1}$ $i=1,2,3,...,d-1$ and $-e_d$ with probabilities $\lambda$, $\mu_1$, $\mu_2$,...,$\mu_d$, where $\{e_1,e_2,..,e_d\}$ are the standard…

Many decision-making processes involve evaluating and then selecting items; examples include scientific peer review, job hiring, school admissions, and investment decisions. The eventual selection is performed by applying rules or…

This paper considers ranking inference of $n$ items based on the observed data on the top choice among $M$ randomly selected items at each trial. This is a useful modification of the Plackett-Luce model for $M$-way ranking with only the top…

We study higher statistical moments of Distortion for randomized social choice in a metric implicit utilitarian model. The Distortion of a social choice mechanism is the expected approximation factor with respect to the optimal utilitarian…

Selection and sorting the Cartesian sum, $X+Y$, are classic and important problems. Here, a new algorithm is presented, which generates the top $k$ values of the form $X_i+Y_j$. The algorithm relies only on median-of-medians and is simple…

This paper proposes a totally asymmetric simple exclusion process on a traveling lane, which is equipped with a queueing system and functions of site assignments along the parking lane. In the proposed system, new particles arrive at the…

This paper proposes an optimal policy that targets the average welfare of the worst-off $\alpha$-fraction of the post-treatment outcome distribution. We refer to this policy as the $\alpha$-Expected Welfare Maximization ($\alpha$-EWM) rule,…

We consider two-dimensional L\'evy processes reflected to stay in the positive quadrant. Our focus is on the non-standard regime when the mean of the free process is negative but the reflection vectors point away from the origin, so that…

This work studies the statistical properties of the maximum penalized likelihood approach in a semi-parametric framework. We recall the penalized likelihood approach for estimating a function and review some asymptotic results. We…

Variable selection over a potentially large set of covariates in a linear model is quite popular. In the Bayesian context, common prior choices can lead to a posterior expectation of the regression coefficients that is a sparse (or nearly…