T paper describes, analyzes and evaluates an algorithm for estimating portfolio loss probabilities using Monte Carlo simulation. Obtaining accurate estimates of such loss probabilities is essential to calculating value-at-risk, which is a quantile of the loss distribution. The method employs a quadratic (’’delta-gamma’’) approximation to the change in portfolio value to guide the selection of e...

Ensemble Conditional Variance Estimation (ECVE) is a novel sufficient dimension reduction (SDR) method in regressions with continuous response and predictors. ECVE applies to general non-additive error regression models operates under the assumption that predictors can be replaced by lower dimensional projection without loss of information. It semiparametric forward model-based exhaustive estim...

Regularized empirical risk minimization (R-ERM) is an important branch of machine learning, since it constrains the capacity of the hypothesis space and guarantees the generalization ability of the learning algorithm. Two classic proximal optimization algorithms, i.e., proximal stochastic gradient descent (ProxSGD) and proximal stochastic coordinate descent (ProxSCD) have been widely used to so...

We provide the first theoretical analysis on the convergence rate of the asynchronous stochastic variance reduced gradient (SVRG) descent algorithm on nonconvex optimization. Recent studies have shown that the asynchronous stochastic gradient descent (SGD) based algorithms with variance reduction converge with a linear convergent rate on convex problems. However, there is no work to analyze asy...