Related papers: Sampling from Arbitrary Functions via PSD Models
We propose a data-driven method to learn the time-dependent probability density of a multivariate stochastic process from sample paths, assuming that the initial probability density is known and can be evaluated. Our method uses a novel…
This paper studies the problem of {\em learning} the probability distribution $P_X$ of a discrete random variable $X$ using indirect and sequential samples. At each time step, we choose one of the possible $K$ functions, $g_1, \ldots, g_K$…
Density power divergence (DPD) is designed to robustly estimate the underlying distribution of observations, in the presence of outliers. However, DPD involves an integral of the power of the parametric density models to be estimated; the…
Random processes play a crucial role in scientific research, often characterized by distribution functions or probability density functions (PDFs). These PDFs serve as essential approximations of the actual and frequently undisclosed…
Given $iid$ observations from an unknown absolute continuous distribution defined on some domain $\Omega$, we propose a nonparametric method to learn a piecewise constant function to approximate the underlying probability density function.…
A method providing optimal estimate of probability density functions (PDFs) from time series is proposed. It allows almost arbitrary resolution PDFs when applied to either, sampled analytic functions or digitized data from experiments. When…
Data subsampling has become widely recognized as a tool to overcome computational and economic bottlenecks in analyzing massive datasets. We contribute to the development of adaptive design for estimation of finite population…
The probability density function (PDF) associated with a given set of samples is approximated by a piecewise-linear polynomial constructed with respect to a binning of the sample space. The kernel functions are a compactly supported basis…
Support Vector Data Description (SVDD) is a popular one-class classifiers for anomaly and novelty detection. But despite its effectiveness, SVDD does not scale well with data size. To avoid prohibitive training times, sampling methods…
Semisupervised methods are techniques for using labeled data $(X_1,Y_1),\ldots,(X_n,Y_n)$ together with unlabeled data $X_{n+1},\ldots,X_N$ to make predictions. These methods invoke some assumptions that link the marginal distribution $P_X$…
A new class of stochastic processes called independent and periodically identically distributed (i.p.i.d.) processes is defined to capture periodically varying statistical behavior. Algorithms are proposed to detect changes in such i.p.i.d.…
Many segmentation tasks, such as medical image segmentation or future state prediction, are inherently ambiguous, meaning that multiple predictions are equally correct. Current methods typically rely on generative models to capture this…
An assumed density approximate likelihood is derived for a class of partially observed stochastic compartmental models which permit observational over-dispersion. This is achieved by treating time-varying reporting probabilities as latent…
We want to approximate general multivariate probability density functions by deterministic sample sets. For optimal sampling, the closeness to the given continuous density has to be assessed. This is a difficult challenge in multivariate…
Deep models are designed to operate on huge volumes of high dimensional data such as images. In order to reduce the volume of data these models must process, we propose a set-based two-stage end-to-end neural subsampling model that is…
Stochastic Differential Equations (SDEs) serve as a powerful modeling tool in various scientific domains, including systems science, engineering, and ecological science. While the specific form of SDEs is typically known for a given…
A method to approximate continuous multi-dimensional probability density functions (PDFs) using their projections and correlations is described. The method is particularly useful for event classification when estimates of systematic…
Nonparametric density estimation is an unsupervised learning problem. In this work we propose a two-step procedure that casts the density estimation problem in the first step into a supervised regression problem. The advantage is that we…
In this paper, we study randomized methods for feedback design of uncertain systems. The first contribution is to derive the sample complexity of various constrained control problems. In particular, we show the key role played by the…
Symmetric positive definite~(SPD) matrices have shown important value and applications in statistics and machine learning, such as FMRI analysis and traffic prediction. Previous works on SPD matrices mostly focus on discriminative models,…