Recent studies have utilized sparse classifications to predict categorical variables from high-dimensional brain activity signals to expose human's intentions and mental states, selecting the relevant features automatically in the model training process. However, existing sparse classification models will likely be prone to the performance degradation which is caused by noise inherent in the brain recordings. To address this issue, we aim to propose a new robust and sparse classification algorithm in this study. To this end, we introduce the correntropy learning framework into the automatic relevance determination based sparse classification model, proposing a new correntropy-based robust sparse logistic regression algorithm. To demonstrate the superior brain activity decoding performance of the proposed algorithm, we evaluate it on a synthetic dataset, an electroencephalogram (EEG) dataset, and a functional magnetic resonance imaging (fMRI) dataset. The extensive experimental results confirm that not only the proposed method can achieve higher classification accuracy in a noisy and high-dimensional classification task, but also it would select those more informative features for the decoding scenarios. Integrating the correntropy learning approach with the automatic relevance determination technique will significantly improve the robustness with respect to the noise, leading to more adequate robust sparse brain decoding algorithm. It provides a more powerful approach in the real-world brain activity decoding and the brain-computer interfaces.

An important unresolved challenge in the theory of regularization is to set the regularization coefficients of popular techniques like the ElasticNet with general provable guarantees. We consider the problem of tuning the regularization parameters of Ridge regression, LASSO, and the ElasticNet across multiple problem instances, a setting that encompasses both cross-validation and multi-task hyperparameter optimization. We obtain a novel structural result for the ElasticNet which characterizes the loss as a function of the tuning parameters as a piecewise-rational function with algebraic boundaries. We use this to bound the structural complexity of the regularized loss functions and show generalization guarantees for tuning the ElasticNet regression coefficients in the statistical setting. We also consider the more challenging online learning setting, where we show vanishing average expected regret relative to the optimal parameter pair. We further extend our results to tuning classification algorithms obtained by thresholding regression fits regularized by Ridge, LASSO, or ElasticNet. Our results are the first general learning-theoretic guarantees for this important class of problems that avoid strong assumptions on the data distribution. Furthermore, our guarantees hold for both validation and popular information criterion objectives.

The COVID-19 pandemic has brought forth the importance of epidemic forecasting for decision makers in multiple domains, ranging from public health to the economy as a whole. While forecasting epidemic progression is frequently conceptualized as being analogous to weather forecasting, however it has some key differences and remains a non-trivial task. The spread of diseases is subject to multiple confounding factors spanning human behavior, pathogen dynamics, weather and environmental conditions. Research interest has been fueled by the increased availability of rich data sources capturing previously unobservable facets and also due to initiatives from government public health and funding agencies. This has resulted, in particular, in a spate of work on 'data-centered' solutions which have shown potential in enhancing our forecasting capabilities by leveraging non-traditional data sources as well as recent innovations in AI and machine learning. This survey delves into various data-driven methodological and practical advancements and introduces a conceptual framework to navigate through them. First, we enumerate the large number of epidemiological datasets and novel data streams that are relevant to epidemic forecasting, capturing various factors like symptomatic online surveys, retail and commerce, mobility, genomics data and more. Next, we discuss methods and modeling paradigms focusing on the recent data-driven statistical and deep-learning based methods as well as on the novel class of hybrid models that combine domain knowledge of mechanistic models with the effectiveness and flexibility of statistical approaches. We also discuss experiences and challenges that arise in real-world deployment of these forecasting systems including decision-making informed by forecasts. Finally, we highlight some challenges and open problems found across the forecasting pipeline.

Lasso and Ridge are important minimization problems in machine learning and statistics. They are versions of linear regression with squared loss where the vector $\theta\in\mathbb{R}^d$ of coefficients is constrained in either $\ell_1$-norm (for Lasso) or in $\ell_2$-norm (for Ridge). We study the complexity of quantum algorithms for finding $\varepsilon$-minimizers for these minimization problems. We show that for Lasso we can get a quadratic quantum speedup in terms of $d$ by speeding up the cost-per-iteration of the Frank-Wolfe algorithm, while for Ridge the best quantum algorithms are linear in $d$, as are the best classical algorithms. As a byproduct of our quantum lower bound for Lasso, we also prove the first classical lower bound for Lasso that is tight up to polylog-factors.

We consider vertical logistic regression (VLR) trained with mini-batch gradient descent -- a setting which has attracted growing interest among industries and proven to be useful in a wide range of applications including finance and medical research. We provide a comprehensive and rigorous privacy analysis of VLR in a class of open-source Federated Learning frameworks, where the protocols might differ between one another, yet a procedure of obtaining local gradients is implicitly shared. We first consider the honest-but-curious threat model, in which the detailed implementation of protocol is neglected and only the shared procedure is assumed, which we abstract as an oracle. We find that even under this general setting, single-dimension feature and label can still be recovered from the other party under suitable constraints of batch size, thus demonstrating the potential vulnerability of all frameworks following the same philosophy. Then we look into a popular instantiation of the protocol based on Homomorphic Encryption (HE). We propose an active attack that significantly weaken the constraints on batch size in the previous analysis via generating and compressing auxiliary ciphertext. To address the privacy leakage within the HE-based protocol, we develop a simple-yet-effective countermeasure based on Differential Privacy (DP), and provide both utility and privacy guarantees for the updated algorithm. Finally, we empirically verify the effectiveness of our attack and defense on benchmark datasets. Altogether, our findings suggest that all vertical federated learning frameworks that solely depend on HE might contain severe privacy risks, and DP, which has already demonstrated its power in horizontal federated learning, can also play a crucial role in the vertical setting, especially when coupled with HE or secure multi-party computation (MPC) techniques.

The efficient treatment for a patient with her/his clinical and other characteristics [1, 2] can be regarded as an important goal of the real personalized medicine. The goal can be achieved by means of the machine learning methods due to the increasing amount of available electronic health records which are a basis for developing accurate models. To estimate the treatment effect, patients are divided into two groups called treatment and control, and then patients from the different groups are compared. One of the popular measures of the efficient treatment used in machine learning models is the average treatment effect (ATE) [3], which is estimated on the basis of observed data about patients as the mean difference between outcomes of patients from the treatment and control groups. Due to the difference between the patients characteristics and the difference between their responses to a particular treatment, the treatment effect is measured by the conditional average treatment effects (CATE) or the heterogeneous treatment effect (HTE) defined as ATE conditional on a patient feature vector [4, 5, 6, 7]. Two main problems can be pointed out when CATE is estimated. The first one is that the control group is usually larger than the treatment group. As a result, we meet the problem of a small training dataset, which does not allow us to apply directly many efficient machine learning methods.

Deep operator learning has emerged as a promising tool for reduced-order modelling and PDE model discovery. Leveraging the expressive power of deep neural networks, especially in high dimensions, such methods learn the mapping between functional state variables. While proposed methods have assumed noise only in the dependent variables, experimental and numerical data for operator learning typically exhibit noise in the independent variables as well, since both variables represent signals that are subject to measurement error. In regression on scalar data, failure to account for noisy independent variables can lead to biased parameter estimates. With noisy independent variables, linear models fitted via ordinary least squares (OLS) will show attenuation bias, wherein the slope will be underestimated. In this work, we derive an analogue of attenuation bias for linear operator regression with white noise in both the independent and dependent variables. In the nonlinear setting, we computationally demonstrate underprediction of the action of the Burgers operator in the presence of noise in the independent variable. We propose error-in-variables (EiV) models for two operator regression methods, MOR-Physics and DeepONet, and demonstrate that these new models reduce bias in the presence of noisy independent variables for a variety of operator learning problems. Considering the Burgers operator in 1D and 2D, we demonstrate that EiV operator learning robustly recovers operators in high-noise regimes that defeat OLS operator learning. We also introduce an EiV model for time-evolving PDE discovery and show that OLS and EiV perform similarly in learning the Kuramoto-Sivashinsky evolution operator from corrupted data, suggesting that the effect of bias in OLS operator learning depends on the regularity of the target operator.

In the third of our article series, we touched on the topic of Linear Regression. We then used this method to create a house price estimator. The concepts of Linear Regression and Logistic Regression should not be confused with each other. Logistic Regression is a Linear Classifier. A statistical method used to analyze a dataset with one or more independent variables that determine a class. The outcome is measured with a binary variable (there are only two possible outcomes).

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This article will explain some of the most well known machine learning algorithms in less than a minute - helping everyone to understand them! One of the simplest Machine learning algorithms out there, Linear Regression is used to make predictions on continuous dependent variables with knowledge from independent variables. A dependent variable is the effect, in which its value depends on changes in the independent variable. You may remember the line of best fit from school - this is what Linear Regression produces. A simple example is predicting one's weight depending on their height.