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In deep image compression, uniform quantization is applied to latent representations obtained by using an auto-encoder architecture for reducing bits and entropy coding. Quantization is a problem encountered in the end-to-end training of…
Particle flow Gaussian particle flow (PFGPF) uses an invertible particle flow to generate a proposal density. It approximates the predictive and posterior distributions as Gaussian densities. In this paper, we use bank of PFGPF filters to…
We give a highly efficient "semi-agnostic" algorithm for learning univariate probability distributions that are well approximated by piecewise polynomial density functions. Let $p$ be an arbitrary distribution over an interval $I$ which is…
This paper describes performance bounds for compressed sensing in the presence of Poisson noise when the underlying signal, a vector of Poisson intensities, is sparse or compressible (admits a sparse approximation). The signal-independent…
The probability density function of Kerr effect phase noise, often called the Gordon-Mollenauer effect, is derived analytically. The Kerr effect phase noise can be accurately modeled as the summation of a Gaussian random variable and a…
This paper introduces a general method to approximate the convolution of an arbitrary program with a Gaussian kernel. This process has the effect of smoothing out a program. Our compiler framework models intermediate values in the program…
We study the behaviour of linear perturbations in multifield coupled quintessence models. Using gauge invariant linear cosmological perturbation theory we provide the full set of governing equations for this class of models, and solve the…
Nonuniform subsampling methods are effective to reduce computational burden and maintain estimation efficiency for massive data. Existing methods mostly focus on subsampling with replacement due to its high computational efficiency. If the…
Generative neural image compression supports data representation at extremely low bitrate, synthesizing details at the client and consistently producing highly realistic images. By leveraging the similarities between quantization error and…
Tensors are multi-way arrays, and the Candecomp/Parafac (CP) tensor factorization has found application in many different domains. The CP model is typically fit using a least squares objective function, which is a maximum likelihood…
We analyze the convergence of probability density functions utilizing approximate models for both forward and inverse problems. We consider the standard forward uncertainty quantification problem where an assumed probability density on…
In this paper we introduce and study fused lasso nearly-isotonic signal approximation, which is a combination of fused lasso and generalized nearly-isotonic regression. We show how these three estimators relate to each other, derive…
Laplace's method approximates a target density with a Gaussian distribution at its mode. It is computationally efficient and asymptotically exact for Bayesian inference due to the Bernstein-von Mises theorem, but for complex targets and…
We develop a computational procedure to estimate the covariance hyperparameters for semiparametric Gaussian process regression models with additive noise. Namely, the presented method can be used to efficiently estimate the variance of the…
We present methods that can provide an exponential savings in the resources required to perform dynamic parameter estimation using quantum systems. The key idea is to merge classical compressive sensing techniques with quantum control…
In probabilistic program analysis, quantitative analysis aims at deriving tight numerical bounds for probabilistic properties such as expectation and assertion probability. Most previous works consider numerical bounds over the whole…
This paper is concerned with scalar quantization of transform coefficients in an audio codec. The generalized Gaussian distribution (GGD) is used as an approximation of one-dimensional probability density function for transform coefficients…
In quantum mechanics, a norm squared wave function can be interpreted as the probability density that describes the likelihood of a particle to be measured in a given position or momentum. This statistical property is at the core of the…
Probabilistic machine learning models are distinguished by their ability to integrate prior knowledge of noise statistics, smoothness parameters, and training data uncertainty. A common approach involves modeling data with Gaussian…
We consider the rate of piecewise constant approximation to a locally stationary process $X(t),t\in [0,1]$, having a variable smoothness index $\alpha(t)$. Assuming that $\alpha(\cdot)$ attains its unique minimum at zero and satisfies the…