In this paper we offer a review and bibliography of work on Hankel low-rank approximation and completion, with particular emphasis on how this methodology can be used for time series analysis and forecasting. We begin by describing possible formulations of the problem and offer commentary on related topics and challenges in obtaining globally optimal solutions. Key theorems are provided, and the paper closes with some expository examples.

Standardized tests play a crucial role in the detection of cognitive impairment. Previous work demonstrated that automatic detection of cognitive impairment is possible using audio data from a standardized picture description task. The presented study goes beyond that, evaluating our methods on data taken from two standardized neuropsychological tests, namely the German SKT and a German version of the CERAD-NB, and a semi-structured clinical interview between a patient and a psychologist. For the tests, we focus on speech recordings of three sub-tests: reading numbers (SKT 3), interference (SKT 7), and verbal fluency (CERAD-NB 1). We show that acoustic features from standardized tests can be used to reliably discriminate cognitively impaired individuals from non-impaired ones. Furthermore, we provide evidence that even features extracted from random speech samples of the interview can be a discriminator of cognitive impairment. In our baseline experiments, we use OpenSMILE features and Support Vector Machine classifiers. In an improved setup, we show that using wav2vec 2.0 features instead, we can achieve an accuracy of up to 85%.

To avoid the curse of dimensionality, a common approach to clustering high-dimensional data is to first project the data into a space of reduced dimension, and then cluster the projected data. Although effective, this two-stage approach prevents joint optimization of the dimensionality-reduction and clustering models, and obscures how well the complete model describes the data. Here, we show how a family of such two-stage models can be combined into a single, hierarchical model that we call a hierarchical mixture of Gaussians (HMoG). An HMoG simultaneously captures both dimensionality-reduction and clustering, and its performance is quantified in closed-form by the likelihood function. By formulating and extending existing models with exponential family theory, we show how to maximize the likelihood of HMoGs with expectation-maximization. We apply HMoGs to synthetic data and RNA sequencing data, and demonstrate how they exceed the limitations of two-stage models. Ultimately, HMoGs are a rigorous generalization of a common statistical framework, and provide researchers with a method to improve model performance when clustering high-dimensional data.

Aleatoric uncertainty quantification seeks for distributional knowledge of random responses, which is important for reliability analysis and robustness improvement in machine learning applications. Previous research on aleatoric uncertainty estimation mainly targets closed-formed conditional densities or variances, which requires strong restrictions on the data distribution or dimensionality. To overcome these restrictions, we study conditional generative models for aleatoric uncertainty estimation. We introduce two metrics to measure the discrepancy between two conditional distributions that suit these models. Both metrics can be easily and unbiasedly computed via Monte Carlo simulation of the conditional generative models, thus facilitating their evaluation and training. We demonstrate numerically how our metrics provide correct measurements of conditional distributional discrepancies and can be used to train conditional models competitive against existing benchmarks.

The theoretical analysis of multi-class classification has proved that the existing multi-class classification methods can train a classifier with high classification accuracy on the test set, when the instances are precise in the training and test sets with same distribution and enough instances can be collected in the training set. However, one limitation with multi-class classification has not been solved: how to improve the classification accuracy of multi-class classification problems when only imprecise observations are available. Hence, in this paper, we propose a novel framework to address a new realistic problem called multi-class classification with imprecise observations (MCIMO), where we need to train a classifier with fuzzy-feature observations. Firstly, we give the theoretical analysis of the MCIMO problem based on fuzzy Rademacher complexity. Then, two practical algorithms based on support vector machine and neural networks are constructed to solve the proposed new problem. Experiments on both synthetic and real-world datasets verify the rationality of our theoretical analysis and the efficacy of the proposed algorithms.

Most dimensionality reduction methods employ frequency domain representations obtained from matrix diagonalization and may not be efficient for large datasets with relatively high intrinsic dimensions. To address this challenge, Correlated Clustering and Projection (CCP) offers a novel data domain strategy that does not need to solve any matrix. CCP partitions high-dimensional features into correlated clusters and then projects correlated features in each cluster into a one-dimensional representation based on sample correlations. Residue-Similarity (R-S) scores and indexes, the shape of data in Riemannian manifolds, and algebraic topology-based persistent Laplacian are introduced for visualization and analysis. Proposed methods are validated with benchmark datasets associated with various machine learning algorithms.

Exponential generalization bounds with near-tight rates have recently been established for uniformly stable learning algorithms. The notion of uniform stability, however, is stringent in the sense that it is invariant to the data-generating distribution. Under the weaker and distribution dependent notions of stability such as hypothesis stability and $L_2$-stability, the literature suggests that only polynomial generalization bounds are possible in general cases. The present paper addresses this long standing tension between these two regimes of results and makes progress towards relaxing it inside a classic framework of confidence-boosting. To this end, we first establish an in-expectation first moment generalization error bound for potentially randomized learning algorithms with $L_2$-stability, based on which we then show that a properly designed subbagging process leads to near-tight exponential generalization bounds over the randomness of both data and algorithm. We further substantialize these generic results to stochastic gradient descent (SGD) to derive improved high-probability generalization bounds for convex or non-convex optimization problems with natural time decaying learning rates, which have not been possible to prove with the existing hypothesis stability or uniform stability based results.

Image Classification is a process of classifying various image categories to their appropriate labels or categories it is associated with. Image classification is mostly employed with Convolutional Neural Networks (CNNs), but this article is an attempt to showcase that even logistic regression has the capability to classify images efficiently with a reduction in computational time and also to waive off the tedious task of building complex models for image classification. Logistic Regression is one of the supervised machine learning algorithms which would be majorly employed for binary class classification problems where according to the occurrence of a particular category of data the outcomes are fixed. Logistic regression operates basically through a sigmoidal function for values ranging between 0 and 1. As mentioned earlier as this article emphasizes using Logistic Regression for Image classification we are using the Hand Sign Digit Classification dataset with two categories of images showing Hand Signs of 0 and 1.

We all know that in Linear Regression we aim to minimise the Sum of Squares Error (SSE) as our objective. However, why is it the SSE and where does this expression even come from? In this article I hope to answer this question using something called the Maximum Likelihood Estimator. Spending enough time in the Data Science community I am confident you would have come across the term Maximum Likelihood Estimator (MLE). I am not going to give a super in detail analysis of MLE, primarily because it has been done so many times in different ways that are probably better than I could ever explain it.

Data Scientists have the role to extract information from raw data. They aren't engineers, nor they are software developers. They dig inside data and extract the gold from the mine. Knowing what a model does and how it works is part of this job. Black-boxes models, although sometimes work better than other models, aren't a good idea if we need to learn something from our data.