Related papers: A simple tool for bounding the deviation of random…
Nonparametric Bayesian models are used routinely as flexible and powerful models of complex data. Many times, a statistician may have additional informative beliefs about data distribution of interest, e.g., its mean or subset components,…
We establish, under a moment matching hypothesis, the local universality of the correlation functions associated with products of $M$ independent iid random matrices, as $M$ is fixed, and the sizes of the matrices tend to infinity. This…
In this paper we show that for the purposes of dimensionality reduction certain class of structured random matrices behave similarly to random Gaussian matrices. This class includes several matrices for which matrix-vector multiply can be…
We show that a tessellation generated by a small number of random affine hyperplanes can be used to approximate Euclidean distances between any two points in an arbitrary bounded set $T$, where the random hyperplanes are generated by…
We consider the problem of encoding a finite set of vectors into a small number of bits while approximately retaining information on the angular distances between the vectors. By deriving improved variance bounds related to binary Gaussian…
In the matrix sensing problem, one wishes to reconstruct a matrix from (possibly noisy) observations of its linear projections along given directions. We consider this model in the high-dimensional limit: while previous works on this model…
Gaussian process is one of the most popular non-parametric Bayesian methodologies for modeling the regression problem. It is completely determined by its mean and covariance functions. And its linear property makes it relatively…
We study the landscape complexity of the Hamiltonian $X_N(x) +\frac\mu2 \|x\|^2,$ where $X_{N}$ is a smooth Gaussian process with isotropic increments on $\mathbb R^{N}$. This model describes a single particle on a random potential in…
We prove two universality results for random tensors of arbitrary rank D. We first prove that a random tensor whose entries are N^D independent, identically distributed, complex random variables converges in distribution in the large N…
Gaussian process is a theoretically appealing model for nonparametric analysis, but its computational cumbersomeness hinders its use in large scale and the existing reduced-rank solutions are usually heuristic. In this work, we propose a…
In this article, we obtain a super-exponential rate of convergence in total variation between the traces of the first $m$ powers of an $n\times n$ random unitary matrices and a $2m$-dimensional Gaussian random variable. This generalizes…
Consider the product $X = X_{1}\cdots X_{m}$ of $m$ independent $n\times n$ iid random matrices. When $m$ is fixed and the dimension $n$ tends to infinity, we prove Gaussian limits for the centered linear spectral statistics of $X$ for…
In this paper, we propose a data based transformation for infinite-dimensional Gaussian processes and derive its limit theorem. For a classification problem, this transformation induces complete separation among the associated Gaussian…
Quadratic variations of Gaussian processes play important role in both stochastic analysis and in applications such as estimation of model parameters, and for this reason the topic has been extensively studied in the literature. In this…
Data-driven models are subject to model errors due to limited and noisy training data. Key to the application of such models in safety-critical domains is the quantification of their model error. Gaussian processes provide such a measure…
Algorithmic Gaussianization is a phenomenon that can arise when using randomized sketching or sampling methods to produce smaller representations of large datasets: For certain tasks, these sketched representations have been observed to…
Variational inference is a powerful tool for approximate inference, and it has been recently applied for representation learning with deep generative models. We develop the variational Gaussian process (VGP), a Bayesian nonparametric…
Bayesian posterior distributions arising in modern applications, including inverse problems in partial differential equation models in tomography and subsurface flow, are often computationally intractable due to the large computational cost…
Machine learning models can be improved by adapting them to respect existing background knowledge. In this paper we consider multitask Gaussian processes, with background knowledge in the form of constraints that require a specific sum of…
The use of Gaussian processes (GPs) is supported by efficient sampling algorithms, a rich methodological literature, and strong theoretical grounding. However, due to their prohibitive computation and storage demands, the use of exact GPs…