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We develop a novel deep learning technique, termed Deep Orthogonal Decomposition (DOD), for dimensionality reduction and reduced order modeling of parameter dependent partial differential equations. The approach consists in the construction…

Current state-of-the-art optimizers are adaptive gradient-based optimization methods such as Adam. Recently, there has been an increasing interest in formulating gradient-based optimizers in a probabilistic framework for better modeling the…

A recent novel extension of multi-output Gaussian processes handles heterogeneous outputs assuming that each output has its own likelihood function. It uses a vector-valued Gaussian process prior to jointly model all likelihoods' parameters…

In statistical mechanics, computing the partition function is generally difficult. An approximation method using a variational autoregressive network (VAN) has been proposed recently. This approach offers the advantage of directly…

Many of the new developments in machine learning are connected with gradient-based optimization methods. Recently, these methods have been studied using a variational perspective. This has opened up the possibility of introducing…

Inspired by dynamic programming, we propose Stochastic Virtual Gradient Descent (SVGD) algorithm where the Virtual Gradient is defined by computational graph and automatic differentiation. The method is computationally efficient and has…

This paper introduces BART-RDD, a sum-of-trees regression model built around a novel regression tree prior, which incorporates the special covariate structure of regression discontinuity designs. Specifically, the tree splitting process is…

The paper develops a general flexible framework for Network Autoregressive Processes (NAR), wherein the response of each node linearly depends on its past values, a prespecified linear combination of neighboring nodes and a set of…

Optimal dividend strategy in dual risk model is well studied in the literatures. But to the best of our knowledge, all the previous works assumes deterministic interest rate. In this paper, we study the optimal dividends strategy in dual…

Autoregressive models have emerged as a powerful approach for visual generation but suffer from slow inference speed due to their sequential token-by-token prediction process. In this paper, we propose a simple yet effective approach for…

Visual Autoregressive Models (VAR) offer efficient and high-quality image generation but suffer from computational redundancy due to repeated Transformer calls at increasing resolutions. We introduce a dynamic Mixture-of-Experts router…

Model order reduction through the POD-Galerkin method can lead to dramatic gains in terms of computational efficiency in solving physical problems. However, the applicability of the method to non linear high-dimensional dynamical systems…

Stochastic dividend discount models (Hurley and Johnson, 1994 and 1998, Yao, 1997) present expressions for the expected value of stock prices when future dividends evolve according to some random scheme. In this paper we try to offer a more…

This paper presents a model order reduction (MOR) approach for high dimensional problems in the analysis of financial risk. To understand the financial risks and possible outcomes, we have to perform several thousand simulations of the…

Jointly modeling and forecasting economic and financial variables across a large set of countries has long been a significant challenge. Two primary approaches have been utilized to address this issue: the vector autoregressive model with…

We propose an artificial market model based on deterministic agents. The agents modify their ask/bid price depending on past price changes. The temporal development of market price fluctuations is calculated numerically. A probability…

Conventional prior for Variational Auto-Encoder (VAE) is a Gaussian distribution. Recent works demonstrated that choice of prior distribution affects learning capacity of VAE models. We propose a general technique…

In recent years, the dynamic factor model has emerged as a dominant tool in economics and finance, particularly for investment strategies. This model offers improved handling of complex, nonlinear, and noisy market conditions compared to…

This paper presents a novel approach that enables autoregressive video generation with high efficiency. We propose to reformulate the video generation problem as a non-quantized autoregressive modeling of temporal frame-by-frame prediction…

Autoregressive models have recently shown great promise in visual generation by leveraging discrete token sequences akin to language modeling. However, existing approaches often suffer from inefficiency, either due to token-by-token…