Related papers: Adaptive stratified Monte Carlo using decision tre…
We discuss the improvement in the accuracy of a Monte Carlo integration that can be obtained by optimization of the `a-priori weights' of the various channels. These channels may be either the strata in a stratified-sampling approach, or…
We propose a Monte Carlo algorithm to sample from high dimensional probability distributions that combines Markov chain Monte Carlo and importance sampling. We provide a careful theoretical analysis, including guarantees on robustness to…
In solving simulation-based stochastic root-finding or optimization problems that involve rare events, such as in extreme quantile estimation, running crude Monte Carlo can be prohibitively inefficient. To address this issue, importance…
Methods of approximate Bayesian computation (ABC) are increasingly used for analysis of complex models. A major challenge for ABC is over-coming the often inherent problem of high rejection rates in the accept/reject methods based on…
We present adaptive sequential SAA (sample average approximation) algorithms to solve large-scale two-stage stochastic linear programs. The iterative algorithm framework we propose is organized into \emph{outer} and \emph{inner} iterations…
In many risk-aware and multi-objective reinforcement learning settings, the utility of the user is derived from the single execution of a policy. In these settings, making decisions based on the average future returns is not suitable. For…
We describe a new algorithm, VEGAS+, for adaptive multidimensional Monte Carlo integration. The new algorithm adds a second adaptive strategy, adaptive stratified sampling, to the adaptive importance sampling that is the basis for its…
We present an algorithm for classification tasks on big data. Experiments conducted as part of this study indicate that the algorithm can be as accurate as ensemble methods such as random forests or gradient boosted trees. Unlike ensemble…
Algorithms for binary classification based on adaptive tree partitioning are formulated and analyzed for both their risk performance and their friendliness to numerical implementation. The algorithms can be viewed as generating a set…
We show that the variance of the Monte Carlo estimator that is importance sampled from an exponential family is a convex function of the natural parameter of the distribution. With this insight, we propose an adaptive importance sampling…
We investigate the stability of a Sequential Monte Carlo (SMC) method applied to the problem of sampling from a target distribution on $\mathbb{R}^d$ for large $d$. It is well known that using a single importance sampling step one produces…
We study the convergence of the predictive surface of regression trees and forests. To support our analysis we introduce a notion of adaptive concentration for regression trees. This approach breaks tree training into a model selection…
Many problems in the physical sciences, machine learning, and statistical inference necessitate sampling from a high-dimensional, multi-modal probability distribution. Markov Chain Monte Carlo (MCMC) algorithms, the ubiquitous tool for this…
This paper concerns the approximation of smooth, high-dimensional functions from limited samples using polynomials. This task lies at the heart of many applications in computational science and engineering - notably, some of those arising…
Regularized linear regression under the $\ell_1$ penalty, such as the Lasso, has been shown to be effective in variable selection and sparse modeling. The sampling distribution of an $\ell_1$-penalized estimator $\hat{\beta}$ is hard to…
Monte Carlo Tree Search (MCTS), most famously used in game-play artificial intelligence (e.g., the game of Go), is a well-known strategy for constructing approximate solutions to sequential decision problems. Its primary innovation is the…
Computing risk measures of a financial portfolio comprising thousands of derivatives is a challenging problem because (a) it involves a nested expectation requiring multiple evaluations of the loss of the financial portfolio for different…
In sampling theory, stratification corresponds to a technique used in surveys, which allows segmenting a population into homogeneous subpopulations (strata) to produce statistics with a higher level of precision. In particular, this article…
Multilevel sampling methods, such as multilevel and multifidelity Monte Carlo, multilevel stochastic collocation, or delayed acceptance Markov chain Monte Carlo, have become standard uncertainty quantification (UQ) tools for a wide class of…
When a Monte Carlo algorithm is used to evaluate a physical observable A, it is possible to slightly modify the algorithm so that it evaluates simultaneously A and the derivatives $\partial$ $\varsigma$ A of A with respect to each…