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Part I of this work [Gao25] establishes online scaled gradient methods (OSGM), a framework that utilizes online convex optimization to adapt stepsizes in gradient methods. This paper focuses on the practical aspects of OSGM. We leverage the…
With the development of data acquisition technology, large amounts of multi-channel data are collected and widely used in many fields. Most of them, such as RGB images and vector fields, can be expressed as different types of multi-channel…
The order of convergence of the Monte Carlo method is 1/2 which means that we need quadruple samples to decrease the error in half in the numerical simulation. Multilevel Monte Carlo methods reach the same order of error by spending less…
Recently, there has been significant progress in the development of distributed first order methods. (At least) two different types of methods, designed from very different perspectives, have been proposed that achieve both exact and linear…
It is important to predict how the Global Mean Temperature (GMT) will evolve in the next few decades. The ability to predict historical data is a necessary first step toward the actual goal of making long-range forecasts. This paper…
We examine an analytic variational inference scheme for the Gaussian Process State Space Model (GPSSM) - a probabilistic model for system identification and time-series modelling. Our approach performs variational inference over both the…
We develop a generalized control function approach to production function estimation. Our approach accommodates settings in which productivity evolves jointly with other unobservable factors such as latent demand shocks and the…
In this talk I discuss a new possibility for stochastic representation of the fe rmion determinant. The method can be used for global Monte Carlo fermion algorit hms and is tested in the case of the Schwinger model.
Functionals in geometric probability are often expressed as sums of bounded functions exhibiting exponential stabilization. Methods based on cumulant techniques and exponential modifications of measures show that such functionals satisfy…
Regression evaluation has been performed for decades. Some metrics have been identified to be robust against shifting and scaling of the data but considering the different distributions of data is much more difficult to address (imbalance…
We study generalized linear prediction under a streaming setting, where each iteration uses only one fresh data point for a gradient-level update. While momentum is well-established in deterministic optimization, a fundamental open question…
In backward error analysis, an approximate solution to an equation is compared to the exact solution to a nearby modified equation. In numerical ordinary differential equations, the two agree up to any power of the step size. If the…
In the context of the analysis of measured data, one is often faced with the task to differentiate data numerically. Typically, this occurs when measured data are concerned or data are evaluated numerically during the evolution of partial…
The construction of low-discrepancy sets, used for uniform sampling and numerical integration, has recently seen great improvements based on optimization and machine learning techniques. However, these methods are computationally expensive,…
We establish a Cram\'er-type moderate deviation result for self-normalized sums of weakly dependent random variables, where the moment requirement is much weaker than the non-self-normalized counterpart. The range of the moderate deviation…
Score-based generative models (SGMs) are powerful tools to sample from complex data distributions. Their underlying idea is to (i) run a forward process for time $T_1$ by adding noise to the data, (ii) estimate its score function, and (iii)…
Variational inference methods for latent variable statistical models have gained popularity because they are relatively fast, can handle large data sets, and have deterministic convergence guarantees. However, in practice it is unclear…
Eye Movement analysis with Hidden Markov Models (EMHMM) is a method for modeling eye fixation sequences using hidden Markov models (HMMs). In this report, we run a simulation study to investigate the estimation error for learning HMMs with…
Based on the method of FGD, we apply the method of adaptive gradient descent which uses different step length at different epoch. Adaptive gradient descent performs much better than FGD in the tests and keeps the guarantee of convergence…
The problem of identifying change points in high-dimensional Gaussian graphical models (GGMs) in an online fashion is of interest, due to new applications in biology, economics and social sciences. The offline version of the problem, where…