Related papers: How to produce discreet Gaussian sequences: Algori…
We introduce a discrete network corresponding to any Gaussian wireless network that is obtained by simply quantizing the received signals and restricting the transmitted signals to a finite precision. Since signals in the discrete network…
While score-based generative models (SGMs) have achieved remarkable success in enormous image generation tasks, their mathematical foundations are still limited. In this paper, we analyze the approximation and generalization of SGMs in…
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…
Diffusion processes are a class of stochastic differential equations (SDEs) providing a rich family of expressive models that arise naturally in dynamic modelling tasks. Probabilistic inference and learning under generative models with…
We investigate the transmission of a secret message from Alice to Bob in the presence of an eavesdropper (Eve) and many of decode-and-forward relay nodes. Each link comprises a set of parallel channels, modeling for example an orthogonal…
We derive rates of contraction of posterior distributions on nonparametric or semiparametric models based on Gaussian processes. The rate of contraction is shown to depend on the position of the true parameter relative to the reproducing…
When comparing approximate Gaussian process (GP) models, it can be helpful to be able to generate data from any GP. If we are interested in how approximate methods perform at scale, we may wish to generate very large synthetic datasets to…
Gaussian Process Networks (GPNs) are a class of directed graphical models which employ Gaussian processes as priors for the conditional expectation of each variable given its parents in the network. The model allows the description of…
The many-to-one interference channel has received interest by virtue of embodying the essence of an interference network while being more tractable than the general K-user interference channel. In this paper, we introduce information…
A random vector $\bx\in \R^n$ is a vector whose coordinates are all random variables. A random vector is called a Gaussian vector if it follows Gaussian distribution. These terminology can also be extended to a random (Gaussian) matrix and…
Pyrosequencing is one of the important next-generation sequencing technologies. We derive the distribution of the number of positive signals in pyrograms of this sequencing technology as a function of flow cycle numbers and nucleotide…
We investigate the secret key agreement from correlated Gaussian sources in which the legitimate parties can use the public communication with limited rate. For the class of protocols with the one-way public communication, we show a closed…
The curse of dimensionality is a common phenomenon which affects analysis of datasets characterized by large numbers of variables associated with each point. Problematic scenarios of this type frequently arise in classification algorithms…
In this paper, we count the number of matrices whose rows generate different $\mathbb{Z}_2\mathbb{Z}_8$ additive codes. This is a natural generalization of the well known Gaussian numbers that count the number of matrices whose rows…
We compute analytically, for large N, the probability distribution of the number of positive eigenvalues (the index N_{+}) of a random NxN matrix belonging to Gaussian orthogonal (\beta=1), unitary (\beta=2) or symplectic (\beta=4)…
In this paper, we consider the product-limit quantile estimator of an unknown quantile function under a censored dependent model. This is a parallel problem to the estimation of the unknown distribution function by the product-limit…
A distributed lossy compression network with $L$ encoders and a decoder is considered. Each encoder observes a source and sends a compressed version to the decoder. The decoder produces a joint reconstruction of target signals with the mean…
A continuous approximation for the results of [1] is obtained. In this approximation the energy distribution is represented in the form of the product of the Gibbs factor and superstatistics factor. The mutual weights of the factors are…
The problem is sequence prediction in the following setting. A sequence $x_1,...,x_n,...$ of discrete-valued observations is generated according to some unknown probabilistic law (measure) $\mu$. After observing each outcome, it is required…
Making good predictions of a physical system using a computer code requires the inputs to be carefully specified. Some of these inputs called control variables have to reproduce physical conditions whereas other inputs, called parameters,…