We analyze the dynamics of streaming stochastic gradient descent (SGD) in the high-dimensional limit when applied to generalized linear models and multi-index models (e.g. logistic regression, phase retrieval) with general data-covariance. In particular, we demonstrate a deterministic equivalent of SGD in the form of a system of ordinary differential equations that describes a wide class of statistics, such as the risk and other measures of sub-optimality. This equivalence holds with overwhelming probability when the model parameter count grows proportionally to the number of data. This framework allows us to obtain learning rate thresholds for stability of SGD as well as convergence guarantees. In addition to the deterministic equivalent, we introduce an SDE with a simplified diffusion coefficient (homogenized SGD) which allows us to analyze the dynamics of general statistics of SGD iterates. Finally, we illustrate this theory on some standard examples and show numerical simulations which give an excellent match to the theory.

Wildfire forecasting problems usually rely on complex grid-based mathematical models, mostly involving Computational fluid dynamics(CFD) and Celluar Automata, but these methods have always been computationally expensive and difficult to deliver a fast decision pattern. In this paper, we provide machine learning based approaches that solve the problem of high computational effort and time consumption. This paper predicts the burning duration of a known wildfire by RF(random forest), KNN, and XGBoost regression models and also image-based, like CNN and Encoder. Model inputs are based on the map of landscape features provided by satellites and the corresponding historical fire data in this area. This model is trained by happened fire data and landform feature maps and tested with the most recent real value in the same area. By processing the input differently to obtain the optimal outcome, the system is able to make fast and relatively accurate future predictions based on landscape images of known fires.

Predicting the performance of highly configurable software systems is the foundation for performance testing and quality assurance. To that end, recent work has been relying on machine/deep learning to model software performance. However, a crucial yet unaddressed challenge is how to cater for the sparsity inherited from the configuration landscape: the influence of configuration options (features) and the distribution of data samples are highly sparse. In this paper, we propose an approach based on the concept of 'divide-and-learn', dubbed $DaL$. The basic idea is that, to handle sample sparsity, we divide the samples from the configuration landscape into distant divisions, for each of which we build a regularized Deep Neural Network as the local model to deal with the feature sparsity. A newly given configuration would then be assigned to the right model of division for the final prediction. Experiment results from eight real-world systems and five sets of training data reveal that, compared with the state-of-the-art approaches, $DaL$ performs no worse than the best counterpart on 33 out of 40 cases (within which 26 cases are significantly better) with up to $1.94\times$ improvement on accuracy; requires fewer samples to reach the same/better accuracy; and producing acceptable training overhead. Practically, $DaL$ also considerably improves different global models when using them as the underlying local models, which further strengthens its flexibility. To promote open science, all the data, code, and supplementary figures of this work can be accessed at our repository: https://github.com/ideas-labo/DaL.

We present an artificial intelligence system to remotely assess the motor performance of individuals with Parkinson's disease (PD). Participants performed a motor task (i.e., tapping fingers) in front of a webcam, and data from 250 global participants were rated by three expert neurologists following the Movement Disorder Society Unified Parkinson's Disease Rating Scale (MDS-UPDRS). The neurologists' ratings were highly reliable, with an intra-class correlation coefficient (ICC) of 0.88. We developed computer algorithms to obtain objective measurements that align with the MDS-UPDRS guideline and are strongly correlated with the neurologists' ratings. Our machine learning model trained on these measures outperformed an MDS-UPDRS certified rater, with a mean absolute error (MAE) of 0.59 compared to the rater's MAE of 0.79. However, the model performed slightly worse than the expert neurologists (0.53 MAE). The methodology can be replicated for similar motor tasks, providing the possibility of evaluating individuals with PD and other movement disorders remotely, objectively, and in areas with limited access to neurological care.

Abstract: The COVID-19 pandemic has initiated a global health emergency, with an exigent need for effective cure. Progressively, drug repurposing is emerging as a promising solution as it saves the time, cost and labor. However, the number of drug candidates that have been identified as being repurposed for the treatment of COVID-19 are still insufficient, so more effective and thorough drug repurposing strategies are required. In this study, we joint the molecular docking with machine learning regression approaches to find some prospective therapeutic candidates for COVID-19 treatment. We screened the 5903 approved drugs for their inhibition by targeting the main protease 3CL of SARS-CoV-2, which is responsible to replicate the virus. Molecular docking is used to calculate the binding affinities of these drugs to the main protease 3CL. We employed several machine learning regression approaches for QSAR modeling to find out some potential drugs with high binding affinity. We shortlisted six favorable drugs and examined their physiochemical and pharmacokinetic properties of these top-ranked selected drugs and their best binding interaction for specific target protease 3CLpro. Our study provides an efficient framework for drug repurposing against COVID-19, and establishes the potential of combining molecular docking with machine learning regression approaches to accelerate the identification of potential therapeutic candidates. Our findings contribute to the larger goal of finding effective cures for COVID-19, which is an acute global health challenge. Keywords: COVID-19; main protease 3CL; drug repurposing; QSAR model; binding affinity; molecular docking 1 Introduction The COVID-19 outbreak has presented an unprecedented worldwide health emergency, with over 687 million confirmed cases and over 6.8 million deaths globally as of May 2023 according to https://www.worldometers.info/coronavirus/. At present, there is no certain drug available to treat COVID-19, and the development of effective cures has become a priority for researchers globally [1]. COVID-19 is triggered by SARS-CoV-2, a positive-sense single-stranded RNA virus that mainly infects the respiratory tract of humans [2]. When the spike protein attaches to the ACE2 receptor on the surface of human cells, the virus enters the cell, and then it utilizes the host's cellular machinery to replicate and spread throughout the body. Figure 1 depicts the life cycle of a coronavirus.

We present an online post-hoc calibration method, called Online Platt Scaling (OPS), which combines the Platt scaling technique with online logistic regression. We demonstrate that OPS smoothly adapts between i.i.d. and non-i.i.d. settings with distribution drift. Further, in scenarios where the best Platt scaling model is itself miscalibrated, we enhance OPS by incorporating a recently developed technique called calibeating to make it more robust. Theoretically, our resulting OPS+calibeating method is guaranteed to be calibrated for adversarial outcome sequences. Empirically, it is effective on a range of synthetic and real-world datasets, with and without distribution drifts, achieving superior performance without hyperparameter tuning. Finally, we extend all OPS ideas to the beta scaling method.

This paper studies the binary classification of unbounded data from ${\mathbb R}^d$ generated under Gaussian Mixture Models (GMMs) using deep ReLU neural networks. We obtain $\unicode{x2013}$ for the first time $\unicode{x2013}$ non-asymptotic upper bounds and convergence rates of the excess risk (excess misclassification error) for the classification without restrictions on model parameters. The convergence rates we derive do not depend on dimension $d$, demonstrating that deep ReLU networks can overcome the curse of dimensionality in classification. While the majority of existing generalization analysis of classification algorithms relies on a bounded domain, we consider an unbounded domain by leveraging the analyticity and fast decay of Gaussian distributions. To facilitate our analysis, we give a novel approximation error bound for general analytic functions using ReLU networks, which may be of independent interest. Gaussian distributions can be adopted nicely to model data arising in applications, e.g., speeches, images, and texts; our results provide a theoretical verification of the observed efficiency of deep neural networks in practical classification problems.

We study the problem of regression in a generalized linear model (GLM) with multiple signals and latent variables. This model, which we call a matrix GLM, covers many widely studied problems in statistical learning, including mixed linear regression, max-affine regression, and mixture-of-experts. In mixed linear regression, each observation comes from one of $L$ signal vectors (regressors), but we do not know which one; in max-affine regression, each observation comes from the maximum of $L$ affine functions, each defined via a different signal vector. The goal in all these problems is to estimate the signals, and possibly some of the latent variables, from the observations. We propose a novel approximate message passing (AMP) algorithm for estimation in a matrix GLM and rigorously characterize its performance in the high-dimensional limit. This characterization is in terms of a state evolution recursion, which allows us to precisely compute performance measures such as the asymptotic mean-squared error. The state evolution characterization can be used to tailor the AMP algorithm to take advantage of any structural information known about the signals. Using state evolution, we derive an optimal choice of AMP `denoising' functions that minimizes the estimation error in each iteration. The theoretical results are validated by numerical simulations for mixed linear regression, max-affine regression, and mixture-of-experts. For max-affine regression, we propose an algorithm that combines AMP with expectation-maximization to estimate intercepts of the model along with the signals. The numerical results show that AMP significantly outperforms other estimators for mixed linear regression and max-affine regression in most parameter regimes.

Recently, in the field of recommendation systems, linear regression (autoencoder) models have been investigated as a way to learn item similarity. In this paper, we show a connection between a linear autoencoder model and ZCA whitening for recommendation data. In particular, we show that the dual form solution of a linear autoencoder model actually has ZCA whitening effects on feature vectors of items, while items are considered as input features in the primal problem of the autoencoder/regression model. We also show the correctness of applying a linear autoencoder to low-dimensional item vectors obtained using embedding methods such as Item2vec to estimate item-item similarities. Our experiments provide preliminary results indicating the effectiveness of whitening low-dimensional item embeddings.

Online learning methods yield sequential regret bounds under minimal assumptions and provide in-expectation risk bounds for statistical learning. However, despite the apparent advantage of online guarantees over their statistical counterparts, recent findings indicate that in many important cases, regret bounds may not guarantee tight high-probability risk bounds in the statistical setting. In this work we show that online to batch conversions applied to general online learning algorithms can bypass this limitation. Via a general second-order correction to the loss function defining the regret, we obtain nearly optimal high-probability risk bounds for several classical statistical estimation problems, such as discrete distribution estimation, linear regression, logistic regression, and conditional density estimation. Our analysis relies on the fact that many online learning algorithms are improper, as they are not restricted to use predictors from a given reference class. The improper nature of our estimators enables significant improvements in the dependencies on various problem parameters. Finally, we discuss some computational advantages of our sequential algorithms over their existing batch counterparts.