相关论文: Improved GM(1,1) model based on Simpson formula an…

We consider the problem of estimating a function $s$ on $[-1,1]^{k}$ for large values of $k$ by looking for some best approximation by composite functions of the form $g\circ u$. Our solution is based on model selection and leads to a very…

Continuous-time approximation of Stochastic Gradient Descent (SGD) is a crucial tool to study its escaping behaviors from stationary points. However, existing stochastic differential equation (SDE) models fail to fully capture these…

Diffusion models generate high-quality synthetic data. They operate by defining a continuous-time forward process which gradually adds Gaussian noise to data until fully corrupted. The corresponding reverse process progressively "denoises"…

Examples with bound information on the regression function and density abound in many real applications. We propose a novel approach for estimating such functions by incorporating the prior knowledge on the bounds. Specially, a Gaussian…

This paper proposes a desparsified GMM estimator for estimating high-dimensional regression models allowing for, but not requiring, many more endogenous regressors than observations. We provide finite sample upper bounds on the estimation…

A generalized Gaussian process model (GGPM) is a unifying framework that encompasses many existing Gaussian process (GP) models, such as GP regression, classification, and counting. In the GGPM framework, the observation likelihood of the…

In this work, we study the numerical approximation of a class of singular fully coupled forward backward stochastic differential equations. These equations have a degenerate forward component and non-smooth terminal condition. They are…

Joint models of longitudinal and event-time data have been extensively studied and applied in many different fields. Estimation of joint models is challenging, most present procedures are computational expensive and have a strict…

Graphical Transformation Models (GTMs) are introduced as a novel approach to effectively model multivariate data with intricate marginals and complex dependency structures semiparametrically, while maintaining interpretability through the…

A novel framework of compressed sensing, namely statistical compressed sensing (SCS), that aims at efficiently sampling a collection of signals that follow a statistical distribution, and achieving accurate reconstruction on average, is…

We propose new continuous-time formulations for first-order stochastic optimization algorithms such as mini-batch gradient descent and variance-reduced methods. We exploit these continuous-time models, together with simple Lyapunov analysis…

Stochastic differential equations (SDEs) or diffusions are continuous-valued continuous-time stochastic processes widely used in the applied and mathematical sciences. Simulating paths from these processes is usually an intractable problem,…

Data-driven Model Predictive Control (MPC), where the system model is learned from data with machine learning, has recently gained increasing interests in the control community. Gaussian Processes (GP), as a type of statistical models, are…

The sparse pseudo-input Gaussian process (SPGP) is a new approximation method for speeding up GP regression in the case of a large number of data points N. The approximation is controlled by the gradient optimization of a small set of M…

Time series modeling is a well-established problem, which often requires that methods (1) expressively represent complicated dependencies, (2) forecast long horizons, and (3) efficiently train over long sequences. State-space models (SSMs)…

Distributed Gaussian process (DGP) is a popular approach to scale GP to big data which divides the training data into some subsets, performs local inference for each partition, and aggregates the results to acquire global prediction. To…

In the current context of Big Data, the nature of many forecasting problems has changed from predicting isolated time series to predicting many time series from similar sources. This has opened up the opportunity to develop competitive…

Gradient optimization algorithms using epochs, that is those based on stochastic gradient descent without replacement (SGDo), are predominantly used to train machine learning models in practice. However, the mathematical theory of SGDo and…

Due to computational constraints, running global climate models (GCMs) for many years requires a lower spatial grid resolution (${\gtrsim}50$ km) than is optimal for accurately resolving important physical processes. Such processes are…

We propose a stochastic conditional gradient method (CGM) for minimizing convex finite-sum objectives formed as a sum of smooth and non-smooth terms. Existing CGM variants for this template either suffer from slow convergence rates, or…