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Slow feature analysis (SFA) is a method for extracting slowly varying features from a quickly varying multidimensional signal. An open source Matlab-implementation sfa-tk makes SFA easily useable. We show here that under certain…

The variational auto-encoder (VAE) is a deep latent variable model that has two neural networks in an autoencoder-like architecture; one of them parameterizes the model's likelihood. Fitting its parameters via maximum likelihood (ML) is…

The randomized singular value decomposition (SVD) is a popular and effective algorithm for computing a near-best rank $k$ approximation of a matrix $A$ using matrix-vector products with standard Gaussian vectors. Here, we generalize the…

Weakly-Supervised Semantic Segmentation (WSSS) segments objects without a heavy burden of dense annotation. While as a price, generated pseudo-masks exist obvious noisy pixels, which result in sub-optimal segmentation models trained over…

We propose a unified framework for estimating low-rank matrices through nonconvex optimization based on gradient descent algorithm. Our framework is quite general and can be applied to both noisy and noiseless observations. In the general…

We propose a spectral viscosity method (SVM) to approximate the incompressible Euler equations driven by a multiplicative noise. We show that SVM solution converges to a dissipative measure-valued martingale solution. These solutions are…

We consider the problems of estimation and optimization of utility-based shortfall risk (UBSR), which is a popular risk measure in finance. In the context of UBSR estimation, we derive a non-asymptotic bound on the mean-squared error of the…

Policy gradient methods are very attractive in reinforcement learning due to their model-free nature and convergence guarantees. These methods, however, suffer from high variance in gradient estimation, resulting in poor sample efficiency.…

We develop a general framework for generating estimators of a given quantity which are unbiased to a given order in the difference between the true value of the underlying quantity and the fiducial position in theory space around which we…

With the availability of high frequency financial data, nonparametric estimation of volatility of an asset return process becomes feasible. A major problem is how to estimate the volatility consistently and efficiently, when the observed…

Stochastic gradient descent (SGD), which dates back to the 1950s, is one of the most popular and effective approaches for performing stochastic optimization. Research on SGD resurged recently in machine learning for optimizing convex loss…

In this paper, we consider estimating spot/instantaneous volatility matrices of high-frequency data collected for a large number of assets. We first combine classic nonparametric kernel-based smoothing with a generalised shrinkage technique…

This paper describes a fast algorithm for recovering low-rank matrices from their linear measurements contaminated with Poisson noise: the Poisson noise Maximum Likelihood Singular Value thresholding (PMLSV) algorithm. We propose a convex…

We consider the high-dimensional linear regression model and assume that a fraction of the measurements are altered by an adversary with complete knowledge of the data and the underlying distribution. We are interested in a scenario where…

Compressed sensing (CS) or sparse signal reconstruction (SSR) is a signal processing technique that exploits the fact that acquired data can have a sparse representation in some basis. One popular technique to reconstruct or approximate the…

Optimization via simulation (OvS) procedures that assume the simulation inputs are generated from the real-world distributions are subject to the risk of selecting a suboptimal solution when the distributions are substituted with input…

A practical challenge for structural estimation is the requirement to accurately minimize a sample objective function which is often non-smooth, non-convex, or both. This paper proposes a simple algorithm designed to find accurate solutions…

This paper considers the problem of robust adaptive efficient estimating of a periodic function in a continuous time regression model with the dependent noises given by a general square integrable semimartingale with a conditionally…

We consider an on-line least squares regression problem with optimal solution $\theta^*$ and Hessian matrix H, and study a time-average stochastic gradient descent estimator of $\theta^*$. For $k\ge2$, we provide an unbiased estimator of…

The generalized singular value decomposition (GSVD) is a valuable tool that has many applications in computational science. However, computing the GSVD for large-scale problems is challenging. Motivated by applications in hyper-differential…