Related papers: Importance Sampling for Minimization of Tail Risks…

Importance sampling (IS) is a powerful Monte Carlo (MC) methodology for approximating integrals, for instance in the context of Bayesian inference. In IS, the samples are simulated from the so-called proposal distribution, and the choice of…

This paper considers the classical problem of sampling with Monte Carlo methods a target rare event distribution defined by a score function that is very expensive to compute. We assume we can build using evaluations of the true score, an…

Understanding the shape of a distribution of data is of interest to people in a great variety of fields, as it may affect the types of algorithms used for that data. We study one such problem in the framework of distribution property…

In modern data analysis, random sampling is an efficient and widely-used strategy to overcome the computational difficulties brought by large sample size. In previous studies, researchers conducted random sampling which is according to the…

In risk management, tail risks are of crucial importance. The quality of a tail model, which is determined by data from an unknown distribution, depends critically on the subset of data used to model the tail. Based on a suitably weighted…

We construct importance sampling schemes for stochastic differential equations with small noise and fast oscillating coefficients. Standard Monte Carlo methods perform poorly for these problems in the small noise limit. With multiscale…

We present novel minibatch stochastic optimization methods for empirical risk minimization problems, the methods efficiently leverage variance reduced first-order and sub-sampled higher-order information to accelerate the convergence speed.…

Gradient descent methods and especially their stochastic variants have become highly popular in the last decade due to their efficiency on big data optimization problems. In this thesis we present the development of data sampling strategies…

The entropic risk measure is widely used in high-stakes decision-making across economics, management science, finance, and safety-critical control systems because it captures tail risks associated with uncertain losses. However, when data…

Feature importance scores are ubiquitous tools for understanding the predictions of machine learning models. However, many popular attribution methods suffer from high instability due to random sampling. Leveraging novel ideas from…

Study samples often differ from the target populations of inference and policy decisions in non-random ways. Researchers typically believe that such departures from random sampling -- due to changes in the population over time and space, or…

Rare events can potentially occur in many applications. When manifested as opportunities to be exploited, risks to be ameliorated, or certain features to be extracted, such events become of paramount significance. Due to their sporadic…

In this paper we propose a technique to reduce the number of function evaluations, which is often the bottleneck of the black-box optimization, in the information geometric optimization (IGO) that is a generic framework of the probability…

This paper investigates asymptotically optimal importance sampling (IS) schemes for pricing European call options under the Heston stochastic volatility model. We focus on two distinct rare-event regimes where standard Monte Carlo methods…

Random forest is effective for prediction tasks but the randomness of tree generation hinders interpretability in feature importance analysis. To address this, we proposed DT-Sampler, a SAT-based method for measuring feature importance in…

We make two closely related theoretical contributions to the use of importance sampling schemes. First, for independent sampling, we prove that the minimax optimal trial distribution coincides with the target if and only if the target…

The use of expectiles in risk management has recently gathered remarkable momentum due to their excellent axiomatic and probabilistic properties. In particular, the class of elicitable law-invariant coherent risk measures only consists of…

In computational science workflows, it is often the case that 1) objective functions for optimization involve multiple simulation outputs, and 2) those simulations can be performed (at least partially) in parallel. In this work, we…

This work studies applications and generalizations of a simple estimation technique that provides exponential concentration under heavy-tailed distributions, assuming only bounded low-order moments. We show that the technique can be used…

The aim of this paper is to introduce a new Monte Carlo method based on importance sampling techniques for the simulation of stochastic differential equations. The main idea is to combine random walk on squares or rectangles methods with…