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Current black-box variational inference (BBVI) methods require the user to make numerous design choices -- such as the selection of variational objective and approximating family -- yet there is little principled guidance on how to do so.…

Previous work, mostly published, developed two-shell recursive trading systems. An inner-shell of Canonical Momenta Indicators (CMI) is adaptively fit to incoming market data. A parameterized trading-rule outer-shell uses the global…

Variational Inference (VI) is a method that approximates a difficult-to-compute posterior density using better behaved distributional families. VI is an alternative to the already well-studied Markov chain Monte Carlo (MCMC) method of…

Many novel notions of "risk" (e.g., CVaR, tilted risk, DRO risk) have been proposed and studied, but these risks are all at least as sensitive as the mean to loss tails on the upside, and tend to ignore deviations on the downside. We study…

We address the challenges of modeling high-frequency integer price changes in financial markets using continuous distributions, particularly the Student's t-distribution. We demonstrate that traditional GARCH models, which rely on…

This thesis evaluates most of the extreme mixture models and methods that have appended in the literature and implements them in the context of finance and insurance. The paper also reviews and studies extreme value theory, time series,…

This work addresses the problem of range-Doppler multiple target detection in a radar system in the presence of slow-time correlated and heavy-tailed distributed clutter. Conventional target detection algorithms assume Gaussian-distributed…

In recent years significant progress has been made in dealing with challenging problems using reinforcement learning.Despite its great success, reinforcement learning still faces challenge in continuous control tasks. Conventional methods…

The value-at-risk of a delta-gamma approximated derivatives portfolio can be computed by numerical integration of the characteristic function. However, while the choice of parameters in any numerical integration scheme is paramount, in…

We show how to reduce the problem of computing VaR and CVaR with Student T return distributions to evaluation of analytical functions of the moments. This allows an analysis of the risk properties of systems to be carefully attributed…

Deep neural networks (DNNs) have demonstrated remarkable performance in many tasks but it often comes at a high computational cost and memory usage. Compression techniques, such as pruning and quantization, are applied to reduce the memory…

Numerical integration (NI) packages commonly used in scientific research are limited to returning the value of a definite integral at the upper integration limit, also commonly referred to as numerical quadrature. These quadrature…

Variational Inference (VI) is an attractive alternative to Markov Chain Monte Carlo (MCMC) due to its computational efficiency in the case of large datasets and/or complex models with high-dimensional parameters. However, evaluating the…

Given a finite collection of stochastic alternatives, we study the problem of sequentially allocating a fixed sampling budget to identify the optimal alternative with a high probability, where the optimal alternative is defined as the one…

This paper presents a novel algorithm to obtain the closed-form anti-derivative of a function using Deep Neural Network architecture. In the past, mathematicians have developed several numerical techniques to approximate the values of…

We develop an extreme value framework for CoVaR centered on $v(q \mid p ; C)$, the copula-adjusted probability level, or equivalently, the CoVaR on the uniform (0,1) scale. We characterize the possible tail regimes of $v(q \mid p ; C)$…

Quantization of weights and activations in Deep Neural Networks (DNNs) is a powerful technique for network compression, and has enjoyed significant attention and success. However, much of the inference-time benefit of quantization is…

We propose and analyze algorithms for distributionally robust optimization of convex losses with conditional value at risk (CVaR) and $\chi^2$ divergence uncertainty sets. We prove that our algorithms require a number of gradient…

Given the high volatility and susceptibility to extreme events in the cryptocurrency market, forecasting tail risk is of paramount importance. Value-at-Risk (VaR), a quantile-based risk measure, is widely used for assessing tail risk and is…

We propose a novel approach for detecting change points in high-dimensional linear regression models. Unlike previous research that relied on strict Gaussian/sub-Gaussian error assumptions and had prior knowledge of change points, we…