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We introduce a notion of bounded variation solution for a new class of nonlinear control systems with ordinary and impulsive controls, in which the drift function depends not only on the state, but also on its past history, through a finite…
Debiased recommendation with a randomized dataset has shown very promising results in mitigating the system-induced biases. However, it still lacks more theoretical insights or an ideal optimization objective function compared with the…
Let $A$ be an $n\times n$ random matrix with i.i.d. entries of zero mean, unit variance and a bounded subgaussian moment. We show that the condition number $s_{\max}(A)/s_{\min}(A)$ satisfies the small ball probability estimate $${\mathbb…
The maximality principle has been a valuable tool in identifying the free-boundary functions that are associated with the solutions to several optimal stopping problems involving one-dimensional time-homogeneous diffusions and their running…
We address the problem of producing a lower bound for the mean of a discrete probability distribution, with known support over a finite set of real numbers, from an iid sample of that distribution. Up to a constant, this is equivalent to…
People are often reluctant to sell a house, or shares of stock, below the price at which they originally bought it. While this is generally not consistent with rational utility maximization, it does reflect two strong empirical regularities…
We study the optimal stopping problem for dynamic risk measures represented by Backward Stochastic Differential Equations (BSDEs) with jumps and its relation with reflected BSDEs (RBSDEs). We first provide general existence, uniqueness and…
The objective of this work is to study continuous-time Markov decision processes on a general Borel state space with both impulsive and continuous controls for the infinite-time horizon discounted cost. The continuous-time controlled…
Determination of posterior probability for go-no-go decision and predictive power are becoming increasingly common for resource optimization in clinical investigation. There are vast published literature on these topics; however, the…
In the report the approach to estimation of quality of planned experiments is considered. This approach is based on the analysis of uncertainty, which will take place under the future hypotheses testing about the existence of a new…
We analyze an irreversible investment decision for a project which yields a flow of future operating profits given by a geometric Brownian motion with unknown drift. In contrast to similar optimal stopping problems with incomplete…
We study problem-dependent rates, i.e., generalization errors that scale near-optimally with the variance, the effective loss, or the gradient norms evaluated at the "best hypothesis." We introduce a principled framework dubbed "uniform…
The classical secretary problem has been generalized over the years into several directions. In this paper we confine our interest to those generalizations which have to do with the more general problem of stopping on a last observation of…
Point identification of causal effects requires strong assumptions that are unreasonable in many practical settings. However, informative bounds on these effects can often be derived under plausible assumptions. Even when these bounds are…
Let $T\$ be a stopping time associated with a sequence of independent random variables $Z_{1},Z_{2},...$ . By applying a suitable change in the probability measure we present relations between the moment or probability generating functions…
We want to find the convex combination $S$ of iid Bernoulli random variables that maximizes $\textbf{P}(S\geq t)$ for a given threshold~$t$. Cs\'oka conjectured that such an $S$ is an average if $t\geq p$, where $p$ is the success…
In the search for statistical dependency rules, a crucial task is to restrict the search space by estimating upper bounds for the goodness of yet undiscovered rules. In this paper, we show that all well-behaving goodness measures achieve…
We provide new upper and lower bounds on the minimum possible ratio of the spectral and Frobenius norms of a (partially) symmetric tensor. In the particular case of general tensors our result recovers a known upper bound. For symmetric…
Transductive conformal prediction addresses the simultaneous prediction for multiple data points. Given a desired confidence level, the objective is to construct a prediction set that includes the true outcomes with the prescribed…
The Chernoff bound is a well-known tool for obtaining a high probability bound on the expectation of a Bernoulli random variable in terms of its sample average. This bound is commonly used in statistical learning theory to upper bound the…