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Many parametric statistical models are not properly normalised and only specified up to an intractable partition function, which renders parameter estimation difficult. Examples of unnormalised models are Gibbs distributions, Markov random…
Random features approach has been widely used for kernel approximation in large-scale machine learning. A number of recent studies have explored data-dependent sampling of features, modifying the stochastic oracle from which random features…
Factor analysis, often regarded as a Bayesian variant of matrix factorization, offers superior capabilities in capturing uncertainty, modeling complex dependencies, and ensuring robustness. As the deep learning era arrives, factor analysis…
One main challenge in time series anomaly detection (TSAD) is the lack of labelled data in many real-life scenarios. Most of the existing anomaly detection methods focus on learning the normal behaviour of unlabelled time series in an…
Principal Component Analysis (PCA) is a very successful dimensionality reduction technique, widely used in predictive modeling. A key factor in its widespread use in this domain is the fact that the projection of a dataset onto its first…
Principal component analysis (PCA) is arguably the most widely used approach for large-dimensional factor analysis. While it is effective when the factors are sufficiently strong, it can be inconsistent when the factors are weak and/or the…
Canonical correlation analysis (CCA) is a classic statistical method for discovering latent co-variation that underpins two or more observed random vectors. Several extensions and variations of CCA have been proposed that have strengthened…
Recent works have shown that supervised models often exploit data artifacts to achieve good test scores while their performance severely degrades on samples outside their training distribution. Contrast sets (Gardneret al., 2020) quantify…
Anomaly detection on attributed networks aims to find the nodes whose behaviors are significantly different from other majority nodes. Generally, network data contains information about relationships between entities, and the anomaly is…
Principal components analysis (PCA) is a classical method for the reduction of dimensionality of data in the form of n observations (or cases) of a vector with p variables. For a simple model of factor analysis type, it is proved that…
Independent Component Analysis (ICA) is a classical method for recovering latent variables with useful identifiability properties. For independent variables, cumulant tensors are diagonal; relaxing independence yields tensors whose zero…
The vanishing ideal is a set of polynomials that takes zero value on the given data points. Originally proposed in computer algebra, the vanishing ideal has been recently exploited for extracting the nonlinear structures of data in many…
The main shortage of principle component analysis (PCA) based anomaly detection models is their interpretability. In this paper, our goal is to propose an interpretable PCA-based model for anomaly detection and interpretation. The propose…
This paper introduces a Projected Principal Component Analysis (Projected-PCA), which employs principal component analysis to the projected (smoothed) data matrix onto a given linear space spanned by covariates. When it applies to…
In the contrastive analysis (CA) setting, machine learning practitioners are specifically interested in discovering patterns that are enriched in a target dataset as compared to a background dataset generated from sources of variation…
Visual contrastive learning aims to learn representations by contrasting similar (positive) and dissimilar (negative) pairs of data samples. The design of these pairs significantly impacts representation quality, training efficiency, and…
Principal Component Analysis (PCA) is a method for estimating a subspace given noisy samples. It is useful in a variety of problems ranging from dimensionality reduction to anomaly detection and the visualization of high dimensional data.…
The essence of unsupervised anomaly detection is to learn the compact distribution of normal samples and detect outliers as anomalies in testing. Meanwhile, the anomalies in real-world are usually subtle and fine-grained in a…
Unnormalized (or energy-based) models provide a flexible framework for capturing the characteristics of data with complex dependency structures. However, the application of standard Bayesian inference methods has been severely limited…
Contrastive learning has recently achieved remarkable success in many domains including graphs. However contrastive loss, especially for graphs, requires a large number of negative samples which is unscalable and computationally prohibitive…