We introduce a new differentially private regression setting we call Private Regression in Multiple Outcomes (PRIMO), inspired the common situation where a data analyst wants to perform a set of $l$ regressions while preserving privacy, where the covariates $X$ are shared across all $l$ regressions, and each regression $i \in [l]$ has a different vector of outcomes $y_i$. While naively applying private linear regression techniques $l$ times leads to a $\sqrt{l}$ multiplicative increase in error over the standard linear regression setting, in Subsection $4.1$ we modify techniques based on sufficient statistics perturbation (SSP) to yield greatly improved dependence on $l$. In Subsection $4.2$ we prove an equivalence to the problem of privately releasing the answers to a special class of low-sensitivity queries we call inner product queries. Via this equivalence, we adapt the geometric projection-based methods from prior work on private query release to the PRIMO setting. Under the assumption the labels $Y$ are public, the projection gives improved results over the Gaussian mechanism when $n < l\sqrt{d}$, with no asymptotic dependence on $l$ in the error. In Subsection $4.3$ we study the complexity of our projection algorithm, and analyze a faster sub-sampling based variant in Subsection $4.4$. Finally in Section $5$ we apply our algorithms to the task of private genomic risk prediction for multiple phenotypes using data from the 1000 Genomes project. We find that for moderately large values of $l$ our techniques drastically improve the accuracy relative to both the naive baseline that uses existing private regression methods and our modified SSP algorithm that doesn't use the projection.

In the last decade, the use of Machine and Deep Learning (MDL) methods in Condensed Matter physics has seen a steep increase in the number of problems tackled and methods employed. A number of distinct MDL approaches have been employed in many different topics; from prediction of materials properties to computation of Density Functional Theory potentials and inter-atomic force fields. In many cases the result is a surrogate model which returns promising predictions but is opaque on the inner mechanisms of its success. On the other hand, the typical practitioner looks for answers that are explainable and provide a clear insight on the mechanisms governing a physical phenomena. In this work, we describe a proposal to use a sophisticated combination of traditional Machine Learning methods to obtain an explainable model that outputs an explicit functional formulation for the material property of interest. We demonstrate the effectiveness of our methodology in deriving a new highly accurate expression for the enthalpy of formation of solid solutions of lanthanides orthophosphates.

In this Machine Learning tutorial we will learn about How to Handle Fake News with Machine Learning. In today's fast-paced digital world, spreading fake news has become a significant concern. With the increasing ease of access to social media platforms and other online sources of information, it has become more challenging to distinguish between real and fake news. In this project-based article, we will learn how to build a machine-learning model to detect fake news accurately. This article was published as a part of the Data Science Blogathon.

An increasing number of software companies have already realized the importance of storing project-related data as valuable sources of information for training prediction models. Such kind of modeling opens the door for the implementation of tailored strategies to increase the accuracy in effort estimation of whole teams of engineers. In this article we review the most recent machine learning approaches used to estimate software development efforts for both, non-agile and agile methodologies. We analyze the benefits of adopting an agile methodology in terms of effort estimation possibilities, such as the modeling of programming patterns and misestimation patterns by individual engineers. We conclude with an analysis of current and future trends, regarding software effort estimation through data-driven predictive models.

In the classic regression problem, the value of a real-valued random variable $Y$ is to be predicted based on the observation of a random vector $X$, taking its values in $\mathbb{R}^d$ with $d\geq 1$ say. The statistical learning problem consists in building a predictive function $\hat{f}:\mathbb{R}^d\to \mathbb{R}$ based on independent copies of the pair $(X,Y)$ so that $Y$ is approximated by $\hat{f}(X)$ with minimum error in the mean-squared sense. Motivated by various applications, ranging from environmental sciences to finance or insurance, special attention is paid here to the case of extreme (i.e. very large) observations $X$. Because of their rarity, they contribute in a negligible manner to the (empirical) error and the predictive performance of empirical quadratic risk minimizers can be consequently very poor in extreme regions. In this paper, we develop a general framework for regression in the extremes. It is assumed that $X$'s conditional distribution given $Y$ belongs to a non parametric class of heavy-tailed probability distributions. It is then shown that an asymptotic notion of risk can be tailored to summarize appropriately predictive performance in extreme regions of the input space. It is also proved that minimization of an empirical and non asymptotic version of this 'extreme risk', based on a fraction of the largest observations solely, yields regression functions with good generalization capacity. In addition, numerical results providing strong empirical evidence of the relevance of the approach proposed are displayed.

In recent years, there has been a flurry of research focusing on the fairness of machine learning models, and in particular on quantifying and eliminating bias against protected subgroups. One line of work generalizes the notion of protected subgroups beyond simple discrete classes by introducing the notion of a "rich subgroup", and seeks to train models that are calibrated or equalize error rates with respect to these richer subgroup classes. Largely orthogonally, local model explanation methods have been developed that given a classifier h and test point x, attribute influence for the prediction h(x) to the individual features of x. This raises a natural question: Do local model explanation methods attribute different feature importance values on average across different protected subgroups, and can we detect these disparities efficiently? If the model places high weight on a given feature in a specific protected subgroup, but not on the dataset overall (or vice versa), this could be a potential indicator of bias in the predictive model or the underlying data generating process, and is at the very least a useful diagnostic that signals the need for a domain expert to delve deeper. In this paper, we formally introduce the notion of feature importance disparity (FID) in the context of rich subgroups, design oracle-efficent algorithms to identify large FID subgroups, and conduct a thorough empirical analysis that establishes auditing for FID as an important method to investigate dataset bias. Our experiments show that across 4 datasets and 4 common feature importance methods our algorithms find (feature, subgroup) pairs that simultaneously: (i) have subgroup feature importance that is often an order of magnitude different than the importance on the dataset as a whole (ii) generalize out of sample, and (iii) yield interesting discussions about potential bias inherent in these datasets.

Randomized Controlled Trials (RCTs) represent a gold standard when developing policy guidelines. However, RCTs are often narrow, and lack data on broader populations of interest. Causal effects in these populations are often estimated using observational datasets, which may suffer from unobserved confounding and selection bias. Given a set of observational estimates (e.g. from multiple studies), we propose a meta-algorithm that attempts to reject observational estimates that are biased. We do so using validation effects, causal effects that can be inferred from both RCT and observational data. After rejecting estimators that do not pass this test, we generate conservative confidence intervals on the extrapolated causal effects for subgroups not observed in the RCT. Under the assumption that at least one observational estimator is asymptotically normal and consistent for both the validation and extrapolated effects, we provide guarantees on the coverage probability of the intervals output by our algorithm. To facilitate hypothesis testing in settings where causal effect transportation across datasets is necessary, we give conditions under which a doubly-robust estimator of group average treatment effects is asymptotically normal, even when flexible machine learning methods are used for estimation of nuisance parameters. We illustrate the properties of our approach on semi-synthetic and real world datasets, and show that it compares favorably to standard meta-analysis techniques.

In statistics, the least absolute shrinkage and selection operator (Lasso) is a regression method that performs both variable selection and regularization. There is a lot of literature available, discussing the statistical properties of the regression coefficients estimated by the Lasso method. However, there lacks a comprehensive review discussing the algorithms to solve the optimization problem in Lasso. In this review, we summarize five representative algorithms to optimize the objective function in Lasso, including the iterative shrinkage threshold algorithm (ISTA), fast iterative shrinkage-thresholding algorithms (FISTA), coordinate gradient descent algorithm (CGDA), smooth L1 algorithm (SLA), and path following algorithm (PFA). Additionally, we also compare their convergence rate, as well as their potential strengths and weakness.

We consider the problem of learning a linear operator $\theta$ between two Hilbert spaces from empirical observations, which we interpret as least squares regression in infinite dimensions. We show that this goal can be reformulated as an inverse problem for $\theta$ with the undesirable feature that its forward operator is generally non-compact (even if $\theta$ is assumed to be compact or of $p$-Schatten class). However, we prove that, in terms of spectral properties and regularisation theory, this inverse problem is equivalent to the known compact inverse problem associated with scalar response regression. Our framework allows for the elegant derivation of dimension-free rates for generic learning algorithms under H\"older-type source conditions. The proofs rely on the combination of techniques from kernel regression with recent results on concentration of measure for sub-exponential Hilbertian random variables. The obtained rates hold for a variety of practically-relevant scenarios in functional regression as well as nonlinear regression with operator-valued kernels and match those of classical kernel regression with scalar response.

Most of the standard image and video codecs are block-based and depending upon the compression ratio the compressed images/videos suffer from different distortions. At low ratios, blurriness is observed and as compression increases blocking artifacts occur. Generally, in order to reduce blockiness, images are low-pass filtered which leads to more blurriness. Also, in bokeh mode images they are commonly seen: blurriness as a result of intentional blurred background while blocking artifact and global blurriness arising due to compression. Therefore, such visual media suffer from both blockiness and blurriness distortions. Along with this, noise is also commonly encountered distortion. Most of the existing works on quality assessment quantify these distortions individually. This paper proposes a methodology to blindly measure overall quality of an image suffering from these distortions, individually as well as jointly. This is achieved by considering the sum of absolute values of low and high-frequency Discrete Frequency Transform (DFT) coefficients defined as sum magnitudes. The number of blocks lying in specific ranges of sum magnitudes including zero-valued AC coefficients and mean of 100 maximum and 100 minimum values of these sum magnitudes are used as feature vectors. These features are then fed to the Machine Learning (ML) based Gaussian Process Regression (GPR) model, which quantifies the image quality. The simulation results show that the proposed method can estimate the quality of images distorted with the blockiness, blurriness, noise and their combinations. It is relatively fast compared to many state-of-art methods, and therefore is suitable for real-time quality monitoring applications.