Related papers: Gaussian Approximation for High Dimensional Time S…
The paper contains results in three areas: First we present a general estimate for tail probabilities of Gaussian quadratic forms with known expectation and variance. Thereafter we analyze the distribution of norms of complex Gaussian…
Estimating a sparse covariance matrix is a fundamental problem in high-dimensional statistics. However, thresholding methods developed for independent data are generally not directly applicable to high-dimensional time series, where…
Gaussian process (GP) predictors are an important component of many Bayesian approaches to machine learning. However, even a straightforward implementation of Gaussian process regression (GPR) requires O(n^2) space and O(n^3) time for a…
Graphical models are commonly used to represent conditional dependence relationships between variables. There are multiple methods available for exploring them from high-dimensional data, but almost all of them rely on the assumption that…
The correlation length-scale next to the noise variance are the most used hyperparameters for the Gaussian processes. Typically, stationary covariance functions are used, which are only dependent on the distances between input points and…
Predicting the dependencies between observations from multiple time series is critical for applications such as anomaly detection, financial risk management, causal analysis, or demand forecasting. However, the computational and numerical…
High dimensional time series are endemic in applications of machine learning such as robotics (sensor data), computational biology (gene expression data), vision (video sequences) and graphics (motion capture data). Practical nonlinear…
Exact Gaussian Process (GP) regression has O(N^3) runtime for data size N, making it intractable for large N. Many algorithms for improving GP scaling approximate the covariance with lower rank matrices. Other work has exploited structure…
We consider the problem of inference for the states and parameters of a continuous-time multitype branching process from partially observed time series data. Exact inference for this class of models, typically using sequential Monte Carlo,…
Graphical models describe associations between variables through the notion of conditional independence. Gaussian graphical models are a widely used class of such models where the relationships are formalized by non-null entries of the…
In a recent paper the author obtained optimal bounds for the strong Gaussian approximation of sums of independent $\R^d$-valued random vectors with finite exponential moments. The results may be considered as generalizations of well-known…
We consider estimation of high-dimensional long-run covariance matrices for time series with nonconstant means, a setting in which conventional estimators can be severely biased. To address this difficulty, we propose a difference-based…
We propose an extensive simulation study to compare some variable selection procedures in a high-dimensional framework. Assuming that the relationship between the actives variables and the response variable is linear, the high-dimensional…
We propose an efficient way to sample from a class of structured multivariate Gaussian distributions which routinely arise as conditional posteriors of model parameters that are assigned a conditionally Gaussian prior. The proposed…
A time-domain test for the assumption of second order stationarity of a functional time series is proposed. The test is based on combining individual cumulative sum tests which are designed to be sensitive to changes in the mean, variance…
Gaussian time-series models are often specified through their spectral density. Such models present several computational challenges, in particular because of the non-sparse nature of the covariance matrix. We derive a fast approximation of…
We consider the classification problem of a high-dimensional mixture of two Gaussians with general covariance matrices. Using the replica method from statistical physics, we investigate the asymptotic behavior of a general class of…
Let $X_1,\dots,X_n$ be independent centered random vectors in $\mathbb{R}^d$. This paper shows that, even when $d$ may grow with $n$, the probability $P(n^{-1/2}\sum_{i=1}^nX_i\in A)$ can be approximated by its Gaussian analog uniformly in…
We consider the problem of Gaussian approximation for the $\kappa$th coordinate of a sum of high-dimensional random vectors. Such a problem has been studied previously for $\kappa=1$ (i.e., maxima). However, in many applications, a general…
Bootstrap methods for estimating the long-run covariance of stationary functional time series are considered. We introduce a versatile bootstrap method that relies on functional principal component analysis, where principal component scores…