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We consider multi-class classification problems for high dimensional data. Following the idea of reduced-rank linear discriminant analysis (LDA), we introduce a new dimension reduction tool with a flavor of supervised principal component…

We initiate the study of differentially private learning in the proportional dimensionality regime, in which the number of data samples $n$ and problem dimension $d$ approach infinity at rates proportional to one another, meaning that…

The Delta method is a classical procedure for quantifying epistemic uncertainty in statistical models, but its direct application to deep neural networks is prevented by the large number of parameters $P$. We propose a low cost variant of…

Data depth is a well-known and useful nonparametric tool for analyzing functional data. It provides a novel way of ranking a sample of curves from the center outwards and defining robust statistics, such as the median or trimmed means. It…

Unsupervised learning of feature representations is a challenging yet important problem for analyzing a large collection of multimedia data that do not have semantic labels. Recently proposed neural network-based unsupervised learning…

Anomaly detection is a branch of data analysis and machine learning which aims at identifying observations that exhibit abnormal behaviour. Be it measurement errors, disease development, severe weather, production quality default(s) (items)…

This paper proposes a hierarchical approximate-factor approach to analyzing high-dimensional, large-scale heterogeneous time series data using distributed computing. The new method employs a multiple-fold dimension reduction procedure using…

Linear discriminant analysis (LDA) is a widely used technique for data classification. The method offers adequate performance in many classification problems, but it becomes inefficient when the data covariance matrix is ill-conditioned.…

Frozen pretrained image representations are widely used for transfer learning: a backbone is kept fixed, feature vectors are extracted, and a lightweight classifier is trained on top. This pipeline usually feeds the full feature vector to…

These notes are an overview of some classical linear methods in Multivariate Data Analysis. This is a good old domain, well established since the 60's, and refreshed timely as a key step in statistical learning. It can be presented as part…

In this article, we develop and investigate a new classifier based on features extracted using spatial depth. Our construction is based on fitting a generalized additive model to the posterior probabilities of the different competing…

Most of the existing methods for anomaly detection use only positive data to learn the data distribution, thus they usually need a pre-defined threshold at the detection stage to determine whether a test instance is an outlier.…

In this work we show that the classification performance of high-dimensional structural MRI data with only a small set of training examples is improved by the usage of dimension reduction methods. We assessed two different dimension…

High dimensional data can have a surprising property: pairs of data points may be easily separated from each other, or even from arbitrary subsets, with high probability using just simple linear classifiers. However, this is more of a rule…

Dimension reduction is often an important step in the analysis of high-dimensional data. PCA is a popular technique to find the best low-dimensional approximation of high-dimensional data. However, classical PCA is very sensitive to…

Motivated by the challenge of using DNA-seq data to identify viruses in human blood samples, we propose a novel classification algorithm called "Radial Distance Weighted Discrimination" (or Radial DWD). This classifier is designed for…

The capability of reliably detecting out-of-distribution samples is one of the key factors in deploying a good classifier, as the test distribution always does not match with the training distribution in most real-world applications. In…

High-dimensional big data appears in many research fields such as image recognition, biology and collaborative filtering. Often, the exploration of such data by classic algorithms is encountered with difficulties due to `curse of…

Linear discriminant analysis (LDA) is a classical method for dimensionality reduction, where discriminant vectors are sought to project data to a lower dimensional space for optimal separability of classes. Several recent papers have…

We explore the application of linear discriminant analysis (LDA) to the features obtained in different layers of pretrained deep convolutional neural networks (CNNs). The advantage of LDA compared to other techniques in dimensionality…