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Non-convex optimization is ubiquitous in modern machine learning. Researchers devise non-convex objective functions and optimize them using off-the-shelf optimizers such as stochastic gradient descent and its variants, which leverage the…
The optimization problem that arises out of the least median of squared residuals method in linear regression is analyzed. To simplify the analysis, the problem is replaced by an equivalent one of minimizing the median of absolute…
It is well known that there are asymmetric dependence structures between financial returns. In this paper we use a new nonparametric measure of local dependence, the local Gaussian correlation, to improve portfolio allocation. We extend the…
The bootstrap algebraic multigrid framework allows for the adaptive construction of algebraic multigrid methods in situations where geometric multigrid methods are not known or not available at all. While there has been some work on…
It is shown that the the popular least squares method of option pricing converges even under very general assumptions. This substantially increases the freedom of creating different implementations of the method, with varying levels of…
Real-world distributed systems and networks are often unreliable and subject to random failures of its components. Such a stochastic behavior affects adversely the complexity of optimization tasks performed routinely upon such systems, in…
This paper explores alternative regression techniques in pricing American put options and compares to the least-squares method (LSM) in Monte Carlo implemented by Longstaff-Schwartz, 2001 which uses least squares to estimate the conditional…
In this paper, we document a novel machine learning based bottom-up approach for static and dynamic portfolio optimization on, potentially, a large number of assets. The methodology applies to general constrained optimization problems and…
We study asymptotic behavior of Monte Carlo method. Local consistency is one of an ideal property of Monte Carlo method. However, it may fail to hold local consistency for several reason. In fact, in practice, it is more important to study…
We study generalization properties of kernel regularized least squares regression based on a partitioning approach. We show that optimal rates of convergence are preserved if the number of local sets grows sufficiently slowly with the…
The Multilevel Monte Carlo (MLMC) method has been applied successfully in a wide range of settings since its first introduction by Giles (2008). When using only two levels, the method can be viewed as a kind of control-variate approach to…
Computing systems interacting with real-world processes must safely and reliably process uncertain data. The Monte Carlo method is a popular approach for computing with such uncertain values. This article introduces a framework for…
Adaptive Monte Carlo methods are recent variance reduction techniques. In this work, we propose a mathematical setting which greatly relaxes the assumptions needed by for the adaptive importance sampling techniques presented by Vazquez-Abad…
Sequential Monte Carlo (SMC) methods are a class of Monte Carlo methods that are used to obtain random samples of a high dimensional random variable in a sequential fashion. Many problems encountered in applications often involve different…
Portfolio optimization is an important process in finance that consists in finding the optimal asset allocation that maximizes expected returns while minimizing risk. When assets are allocated in discrete units, this is a combinatorial…
We consider the problem of selecting a portfolio of assets that provides the investor a suitable balance of expected return and risk. With respect to the seminal mean-variance model of Markowitz, we consider additional constraints on the…
Markov Chain Monte Carlo (MCMC) sampling methods are widely used but often encounter either slow convergence or biased sampling when applied to multimodal high dimensional distributions. In this paper, we present a general framework of…
The Sharpe ratio is an important and widely-used risk-adjusted return in financial engineering. In modern portfolio management, one may require an m-sparse (no more than m active assets) portfolio to save managerial and financial costs.…
We consider Monte Carlo approximations to the maximum likelihood estimator in models with intractable norming constants. This paper deals with adaptive Monte Carlo algorithms, which adjust control parameters in the course of simulation. We…
We describe an embarrassingly parallel, anytime Monte Carlo method for likelihood-free models. The algorithm starts with the view that the stochasticity of the pseudo-samples generated by the simulator can be controlled externally by a…