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We address challenges in variable selection with highly correlated data that are frequently present in finance, economics, but also in complex natural systems as e.g. weather. We develop a robustified version of the knockoff framework,…
As the volume and complexity of data continue to expand across various scientific disciplines, the need for robust methods to account for the multiplicity of comparisons has grown widespread. A popular measure of type 1 error rate in…
Calibration is commonly evaluated by comparing model confidence with its empirical correctness, implicitly treating reliability as a function of the confidence score alone. However, this view can hide substantial structure: models may be…
The decreasing cost and improved sensor and monitoring system technology (e.g. fiber optics and strain gauges) have led to more measurements in close proximity to each other. When using such spatially dense measurement data in Bayesian…
We study principal components regression (PCR) in an asymptotic high-dimensional regression setting, where the number of data points is proportional to the dimension. We derive exact limiting formulas for the estimation and prediction…
To construct models of large, multivariate complex systems, such as those in biology, one needs to constrain which variables are allowed to interact. This can be viewed as detecting "local" structures among the variables. In the context of…
With the proliferation of increasingly complicated Deep Learning architectures, data synthesis is a highly promising technique to address the demand of data-hungry models. However, reliably assessing the quality of a 'synthesiser' model's…
Identifying dependency between two random variables is a fundamental problem. The clear interpretability and ability of a procedure to provide information on the form of possible dependence is particularly important when exploring…
Two major research tasks lie at the heart of high dimensional data analysis: accurate parameter estimation and correct support recovery. The existing literature mostly aims for either the best parameter estimation or the best model…
We consider detection and localization of an abrupt break in the covariance structure of high-dimensional random data. The paper proposes a novel testing procedure for this problem. Due to its nature, the approach requires a properly chosen…
The problem of multiple hypothesis testing arises when there are more than one hypothesis to be tested simultaneously for statistical significance. This is a very common situation in many data mining applications. For instance, assessing…
This paper considers the problems of detecting a change point and estimating the location in the correlation matrices of a sequence of high-dimensional vectors, where the dimension is large enough to be comparable to the sample size or even…
We consider the problem of asynchronous online testing, aimed at providing control of the false discovery rate (FDR) during a continual stream of data collection and testing, where each test may be a sequential test that can start and stop…
Biclustering is a method for detecting homogeneous submatrices in a given observed matrix, and it is an effective tool for relational data analysis. Although there are many studies that estimate the underlying bicluster structure of a…
Precision matrices play important roles in many practical applications. Motivated by temporally dependent multivariate data in modern social and scientific studies, we consider the statistical inference of precision matrices for…
This paper aims to develop an effective model-free inference procedure for high-dimensional data. We first reformulate the hypothesis testing problem via sufficient dimension reduction framework. With the aid of new reformulation, we…
Principal component analysis is a useful dimension reduction and data visualization method. However, in high dimension, low sample size asymptotic contexts, where the sample size is fixed and the dimension goes to infinity,a paradox has…
We establish the limiting spectral distribution of Kendall's correlation matrices in the moderate high-dimensional regime where the dimension grows slower than the sample size. Our framework allows observations to be independent but not…
This article studies bootstrap inference for high dimensional weakly dependent time series in a general framework of approximately linear statistics. The following high dimensional applications are covered: (1) uniform confidence band for…
Some high-dimensional data.sets can be modelled by assuming that there are many different linear constraints, each of which is Frequently Approximately Satisfied (FAS) by the data. The probability of a data vector under the model is then…