In our first case study, predicting house prices, you will create models that predict a continuous value (price) from input features (square footage, number of bedrooms and bathrooms,...). This is just one of the many places where regression can be applied. Other applications range from predicting health outcomes in medicine, stock prices in finance, and power usage in high-performance computing, to analyzing which regulators are important for gene expression. In this course, you will explore regularized linear regression models for the task of prediction and feature selection. You will be able to handle very large sets of features and select between models of various complexity.

The theoretical advances on the properties of scoring rules over the past decades have broadened the use of scoring rules in probabilistic forecasting. In meteorological forecasting, statistical postprocessing techniques are essential to improve the forecasts made by deterministic physical models. Numerous state-of-the-art statistical postprocessing techniques are based on distributional regression evaluated with the Continuous Ranked Probability Score (CRPS). However, theoretical properties of such evaluation with the CRPS have solely considered the unconditional framework (i.e. without covariates) and infinite sample sizes. We extend these results and study the rate of convergence in terms of CRPS of distributional regression methods. We find the optimal minimax rate of convergence for a given class of distributions and show that the k-nearest neighbor method and the kernel method reach this optimal minimax rate.

Despite the empirical successes of self-supervised learning (SSL) methods, it is unclear what characteristics of their representations lead to high downstream accuracies. In this work, we characterize properties that SSL representations should ideally satisfy. Specifically, we prove necessary and sufficient conditions such that for any task invariant to given data augmentations, desired probes (e.g., linear or MLP) trained on that representation attain perfect accuracy. These requirements lead to a unifying conceptual framework for improving existing SSL methods and deriving new ones. For contrastive learning, our framework prescribes simple but significant improvements to previous methods such as using asymmetric projection heads. For non-contrastive learning, we use our framework to derive a simple and novel objective. Our resulting SSL algorithms outperform baselines on standard benchmarks, including SwAV+multicrops on linear probing of ImageNet.

Global pooling is one of the most significant operations in many machine learning models and tasks, which works for information fusion and structured data (like sets and graphs) representation. However, without solid mathematical fundamentals, its practical implementations often depend on empirical mechanisms and thus lead to sub-optimal, even unsatisfactory performance. In this work, we develop a novel and generalized global pooling framework through the lens of optimal transport. The proposed framework is interpretable from the perspective of expectation-maximization. Essentially, it aims at learning an optimal transport across sample indices and feature dimensions, making the corresponding pooling operation maximize the conditional expectation of input data. We demonstrate that most existing pooling methods are equivalent to solving a regularized optimal transport (ROT) problem with different specializations, and more sophisticated pooling operations can be implemented by hierarchically solving multiple ROT problems. Making the parameters of the ROT problem learnable, we develop a family of regularized optimal transport pooling (ROTP) layers. We implement the ROTP layers as a new kind of deep implicit layer. Their model architectures correspond to different optimization algorithms. We test our ROTP layers in several representative set-level machine learning scenarios, including multi-instance learning (MIL), graph classification, graph set representation, and image classification. Experimental results show that applying our ROTP layers can reduce the difficulty of the design and selection of global pooling -- our ROTP layers may either imitate some existing global pooling methods or lead to some new pooling layers fitting data better. The code is available at \url{https://github.com/SDS-Lab/ROT-Pooling}.

In post-covid19 world, radio frequency (RF)-based non-contact methods, e.g., software-defined radios (SDR)-based methods have emerged as promising candidates for intelligent remote sensing of human vitals, and could help in containment of contagious viruses like covid19. To this end, this work utilizes the universal software radio peripherals (USRP)-based SDRs along with classical machine learning (ML) methods to design a non-contact method to monitor different breathing abnormalities. Under our proposed method, a subject rests his/her hand on a table in between the transmit and receive antennas, while an orthogonal frequency division multiplexing (OFDM) signal passes through the hand. Subsequently, the receiver extracts the channel frequency response (basically, fine-grained wireless channel state information), and feeds it to various ML algorithms which eventually classify between different breathing abnormalities. Among all classifiers, linear SVM classifier resulted in a maximum accuracy of 88.1\%. To train the ML classifiers in a supervised manner, data was collected by doing real-time experiments on 4 subjects in a lab environment. For label generation purpose, the breathing of the subjects was classified into three classes: normal, fast, and slow breathing. Furthermore, in addition to our proposed method (where only a hand is exposed to RF signals), we also implemented and tested the state-of-the-art method (where full chest is exposed to RF radiation). The performance comparison of the two methods reveals a trade-off, i.e., the accuracy of our proposed method is slightly inferior but our method results in minimal body exposure to RF radiation, compared to the benchmark method.

The cyber-physical convergence is opening up new business opportunities for industrial operators. The need for deep integration of the cyber and the physical worlds establishes a rich business agenda towards consolidating new system and network engineering approaches. This revolution would not be possible without the rich and heterogeneous sources of data, as well as the ability of their intelligent exploitation, mainly due to the fact that data will serve as a fundamental resource to promote Industry 4.0. One of the most fruitful research and practice areas emerging from this data-rich, cyber-physical, smart factory environment is the data-driven process monitoring field, which applies machine learning methodologies to enable predictive maintenance applications. In this paper, we examine popular time series forecasting techniques as well as supervised machine learning algorithms in the applied context of Industry 4.0, by transforming and preprocessing the historical industrial dataset of a packing machine's operational state recordings (real data coming from the production line of a manufacturing plant from the food and beverage domain). In our methodology, we use only a single signal concerning the machine's operational status to make our predictions, without considering other operational variables or fault and warning signals, hence its characterization as ``agnostic''. In this respect, the results demonstrate that the adopted methods achieve a quite promising performance on three targeted use cases.

Independent component analysis (ICA) is a blind source separation method to recover source signals of interest from their mixtures. Most existing ICA procedures assume independent sampling. Second-order-statistics-based source separation methods have been developed based on parametric time series models for the mixtures from the autocorrelated sources. However, the second-order-statistics-based methods cannot separate the sources accurately when the sources have temporal autocorrelations with mixed spectra. To address this issue, we propose a new ICA method by estimating spectral density functions and line spectra of the source signals using cubic splines and indicator functions, respectively. The mixed spectra and the mixing matrix are estimated by maximizing the Whittle likelihood function. We illustrate the performance of the proposed method through simulation experiments and an EEG data application. The numerical results indicate that our approach outperforms existing ICA methods, including SOBI algorithms. In addition, we investigate the asymptotic behavior of the proposed method.

The performance of decision policies and prediction models often deteriorates when applied to environments different from the ones seen during training. To ensure reliable operation, we propose and analyze the stability of a system under distribution shift, which is defined as the smallest change in the underlying environment that causes the system's performance to deteriorate beyond a permissible threshold. In contrast to standard tail risk measures and distributionally robust losses that require the specification of a plausible magnitude of distribution shift, the stability measure is defined in terms of a more intuitive quantity: the level of acceptable performance degradation. We develop a minimax optimal estimator of stability and analyze its convergence rate, which exhibits a fundamental phase shift behavior. Our characterization of the minimax convergence rate shows that evaluating stability against large performance degradation incurs a statistical cost. Empirically, we demonstrate the practical utility of our stability framework by using it to compare system designs on problems where robustness to distribution shift is critical.

Microfinance, despite its significant potential for poverty reduction, is facing sustainability hardships due to high default rates. Although many methods in regular finance can estimate credit scores and default probabilities, these methods are not directly applicable to microfinance due to the following unique characteristics: a) under-explored (developing) areas such as rural Africa do not have sufficient prior loan data for microfinance institutions (MFIs) to establish a credit scoring system; b) microfinance applicants may have difficulty providing sufficient information for MFIs to accurately predict default probabilities; and c) many MFIs use group liability (instead of collateral) to secure repayment. Here, we present a novel control-theoretic model of microfinance that accounts for these characteristics. We construct an algorithm to learn microfinance decision policies that achieve financial inclusion, fairness, social welfare, and sustainability. We characterize the convergence conditions to Pareto-optimum and the convergence speeds. We demonstrate, in numerous real and synthetic datasets, that the proposed method accounts for the complexities induced by group liability to produce robust decisions before sufficient loans are given to establish credit scoring systems and for applicants whose default probability cannot be accurately estimated due to missing information. To the best of our knowledge, this paper is the first to connect microfinance and control theory. We envision that the connection will enable safe learning and control techniques to help modernize microfinance and alleviate poverty.

We propose a novel model agnostic data-driven reliability analysis framework for time-dependent reliability analysis. The proposed approach -- referred to as MAntRA -- combines interpretable machine learning, Bayesian statistics, and identifying stochastic dynamic equation to evaluate reliability of stochastically-excited dynamical systems for which the governing physics is \textit{apriori} unknown. A two-stage approach is adopted: in the first stage, an efficient variational Bayesian equation discovery algorithm is developed to determine the governing physics of an underlying stochastic differential equation (SDE) from measured output data. The developed algorithm is efficient and accounts for epistemic uncertainty due to limited and noisy data, and aleatoric uncertainty because of environmental effect and external excitation. In the second stage, the discovered SDE is solved using a stochastic integration scheme and the probability failure is computed. The efficacy of the proposed approach is illustrated on three numerical examples. The results obtained indicate the possible application of the proposed approach for reliability analysis of in-situ and heritage structures from on-site measurements.