Self-distillation (SD) is the process of first training a \enquote{teacher} model and then using its predictions to train a \enquote{student} model with the \textit{same} architecture. Specifically, the student's objective function is $\big(\xi*\ell(\text{teacher's predictions}, \text{ student's predictions}) + (1-\xi)*\ell(\text{given labels}, \text{ student's predictions})\big)$, where $\ell$ is some loss function and $\xi$ is some parameter $\in [0,1]$. Empirically, SD has been observed to provide performance gains in several settings. In this paper, we theoretically characterize the effect of SD in two supervised learning problems with \textit{noisy labels}. We first analyze SD for regularized linear regression and show that in the high label noise regime, the optimal value of $\xi$ that minimizes the expected error in estimating the ground truth parameter is surprisingly greater than 1. Empirically, we show that $\xi > 1$ works better than $\xi \leq 1$ even with the cross-entropy loss for several classification datasets when 50\% or 30\% of the labels are corrupted. Further, we quantify when optimal SD is better than optimal regularization. Next, we analyze SD in the case of logistic regression for binary classification with random label corruption and quantify the range of label corruption in which the student outperforms the teacher in terms of accuracy. To our knowledge, this is the first result of its kind for the cross-entropy loss.

Soiling is the accumulation of dirt in solar panels which leads to a decreasing trend in solar energy yield and may be the cause of vast revenue losses. The effect of soiling can be reduced by washing the panels, which is, however, a procedure of non-negligible cost. Moreover, soiling monitoring systems are often unreliable or very costly. We study the problem of estimating the soiling ratio in photo-voltaic (PV) modules, i.e., the ratio of the real power output to the power output that would be produced if solar panels were clean. A key advantage of our algorithms is that they estimate soiling, without needing to train on labelled data, i.e., periods of explicitly monitoring the soiling in each park, and without relying on generic analytical formulas which do not take into account the peculiarities of each installation. We consider as input a time series comprising a minimum set of measurements, that are available to most PV park operators. Our experimental evaluation shows that we significantly outperform current state-of-the-art methods for estimating soiling ratio.

This work describes experiments on thermal dynamics of pure H2O excited by hydrodynamic cavitation, which has been reported to facilitate the spin conversion of para- and ortho-isomers at water interfaces. Previous measurements by NMR and capillary methods of excited samples demonstrated changes of proton density by 12-15%, the surface tension up to 15.7%, which can be attributed to a non-equilibrium para-/ortho- ratio. Beside these changes, we also expect a variation of heat capacity. Experiments use a differential calorimetric approach with two devices: one with an active thermostat for diathermic measurements, another is fully passive for long-term measurements. Samples after excitation are degassed at -0.09MPa and thermally equalized in a water bath. Conducted attempts demonstrated changes in the heat capacity of experimental samples by 4.17%--5.72% measured in the transient dynamics within 60 min after excitation, which decreases to 2.08% in the steady-state dynamics 90-120 min after excitation. Additionally, we observed occurrence of thermal fluctuations at the level of 10^-3 C relative temperature on 20-40 min mesoscale dynamics and a long-term increase of such fluctuations in experimental samples. Obtained results are reproducible in both devices and are supported by previously published outcomes on four-photon scattering spectra in the range from -1.5 to 1.5 cm^-1 and electrochemical reactivity in CO2 and H2O2 pathways. Based on these results, we propose a hypothesis about ongoing spin conversion process on mesoscopic scales under weak influx of energy caused by thermal, EM or geomagnetic factors; this enables explaining electrochemical and thermal anomalies observed in long-term measurements.

We developed an inherently interpretable multilevel Bayesian framework for representing variation in regression coefficients that mimics the piecewise linearity of ReLU-activated deep neural networks. We used the framework to formulate a survival model for using medical claims to predict hospital readmission and death that focuses on discharge placement, adjusting for confounding in estimating causal local average treatment effects. We trained the model on a 5% sample of Medicare beneficiaries from 2008 and 2011, based on their 2009--2011 inpatient episodes, and then tested the model on 2012 episodes. The model scored an AUROC of approximately 0.76 on predicting all-cause readmissions -- defined using official Centers for Medicare and Medicaid Services (CMS) methodology -- or death within 30-days of discharge, being competitive against XGBoost and a Bayesian deep neural network, demonstrating that one need-not sacrifice interpretability for accuracy. Crucially, as a regression model, we provide what blackboxes cannot -- the exact gold-standard global interpretation of the model, identifying relative risk factors and quantifying the effect of discharge placement. We also show that the posthoc explainer SHAP fails to provide accurate explanations.

Objectives: To quantify the magnitude of spinal deformity in adolescent idiopathic scoliosis (AIS), the Cobb angle is measured on X-ray images of the spine. Continuous exposure to X-ray radiation to follow-up the progression of scoliosis may lead to negative side effects on patients. Furthermore, manual measurement of the Cobb angle could lead to up to 10{\deg} or more of a difference due to intra/inter observer variation. Therefore, the objective of this study is to identify the Cobb angle by developing an automated radiation-free model, using Machine learning algorithms. Methods: Thirty participants with lumbar/thoracolumbar AIS (15{\deg} < Cobb angle < 66{\deg}) performed gait cycles. The lumbosacral (L5-S1) joint efforts during six gait cycles of participants were used as features to feed training algorithms. Various regression algorithms were implemented and run. Results: The decision tree regression algorithm achieved the best result with the mean absolute error equal to 4.6{\deg} of averaged 10-fold cross-validation. Conclusions: This study shows that the lumbosacral joint efforts during gait as radiation-free data are capable to identify the Cobb angle by using Machine learning algorithms. The proposed model can be considered as an alternative, radiation-free method to X-ray radiography to assist clinicians in following-up the progression of AIS.

We consider the problem of mixed linear regression (MLR), where each observed sample belongs to one of $K$ unknown linear models. In practical applications, the proportions of the $K$ components are often imbalanced. Unfortunately, most MLR methods do not perform well in such settings. Motivated by this practical challenge, in this work we propose Mix-IRLS, a novel, simple and fast algorithm for MLR with excellent performance on both balanced and imbalanced mixtures. In contrast to popular approaches that recover the $K$ models simultaneously, Mix-IRLS does it sequentially using tools from robust regression. Empirically, Mix-IRLS succeeds in a broad range of settings where other methods fail. These include imbalanced mixtures, small sample sizes, presence of outliers, and an unknown number of models $K$. In addition, Mix-IRLS outperforms competing methods on several real-world datasets, in some cases by a large margin. We complement our empirical results by deriving a recovery guarantee for Mix-IRLS, which highlights its advantage on imbalanced mixtures.

The Machine Learning Specialization is a foundational online program created in collaboration between DeepLearning.AI and Stanford Online. This beginner-friendly program will teach you the fundamentals of machine learning and how to use these techniques to build real-world AI applications. This Specialization is taught by Andrew Ng, an AI visionary who has led critical research at Stanford University and groundbreaking work at Google Brain, Baidu, and Landing.AI to advance the AI field. This 3-course Specialization is an updated version of Andrew's pioneering Machine Learning course, rated 4.9 out of 5 and taken by over 4.8 million learners since it launched in 2012. It provides a broad introduction to modern machine learning, including supervised learning (multiple linear regression, logistic regression, neural networks, and decision trees), unsupervised learning (clustering, dimensionality reduction, recommender systems), and some of the best practices used in Silicon Valley for artificial intelligence and machine learning innovation (evaluating and tuning models, taking a data-centric approach to improving performance, and more.)

While many organizations have shifted to working remotely during the COVID-19 pandemic, how the remote workforce and the remote teams are influenced by and would respond to this and future shocks remain largely unknown. Software developers have relied on remote collaborations long before the pandemic, working in virtual teams (GitHub repositories). The dynamics of these repositories through the pandemic provide a unique opportunity to understand how remote teams react under shock. This work presents a systematic analysis. We measure the overall effect of the early pandemic on public GitHub repositories by comparing their sizes and productivity with the counterfactual outcomes forecasted as if there were no pandemic. We find that the productivity level and the number of active members of these teams vary significantly during different periods of the pandemic. We then conduct a finer-grained investigation and study the heterogeneous effects of the shock on individual teams. We find that the resilience of a team is highly correlated to certain properties of the team before the pandemic. Through a bootstrapped regression analysis, we reveal which types of teams are robust or fragile to the shock.

We study the error of linear regression in the face of adversarial attacks. In this framework, an adversary changes the input to the regression model in order to maximize the prediction error. We provide bounds on the prediction error in the presence of an adversary as a function of the parameter norm and the error in the absence of such an adversary. We show how these bounds make it possible to study the adversarial error using analysis from non-adversarial setups. The obtained results shed light on the robustness of overparameterized linear models to adversarial attacks. Adding features might be either a source of additional robustness or brittleness. On the one hand, we use asymptotic results to illustrate how double-descent curves can be obtained for the adversarial error. On the other hand, we derive conditions under which the adversarial error can grow to infinity as more features are added, while at the same time, the test error goes to zero. We show this behavior is caused by the fact that the norm of the parameter vector grows with the number of features. It is also established that $\ell_\infty$ and $\ell_2$-adversarial attacks might behave fundamentally differently due to how the $\ell_1$ and $\ell_2$-norms of random projections concentrate. We also show how our reformulation allows for solving adversarial training as a convex optimization problem. This fact is then exploited to establish similarities between adversarial training and parameter-shrinking methods and to study how the training might affect the robustness of the estimated models.

This paper explores connections between margin-based loss functions and consistency in binary classification and regression applications. It is shown that a large class of margin-based loss functions for binary classification/regression result in estimating scores equivalent to log-likelihood scores weighted by an even function. A simple characterization for conformable (consistent) loss functions is given, which allows for straightforward comparison of different losses, including exponential loss, logistic loss, and others. The characterization is used to construct a new Huber-type loss function for the logistic model. A simple relation between the margin and standardized logistic regression residuals is derived, demonstrating that all margin-based loss can be viewed as loss functions of squared standardized logistic regression residuals. The relation provides new, straightforward interpretations for exponential and logistic loss, and aids in understanding why exponential loss is sensitive to outliers. In particular, it is shown that minimizing empirical exponential loss is equivalent to minimizing the sum of squared standardized logistic regression residuals. The relation also provides new insight into the AdaBoost algorithm.