Fairness has emerged as a key issue in machine learning as it is increasingly used in areas like hiring [Dastin, 2018], healthcare[Gupta and Mohammad, 2017], and criminal justice [Equivant, 2019]. In particular, models' predictions should not lead to decisions that discriminate on the basis of a legally protected attribute, such as race or gender. Among the proposals to address this issue, a growing body of work focuses on learning et al., 2017, del Barrio et al., 2018, Feldmanfair representations of data for downstream modeling [Calmon 2015, Johndrow and Lum, 2019, Kamiran and Calders, 2012]. Most of these approaches are modelet al., agnostic, which provides flexibility when working with the learned representations, but comes at the cost of potentially suboptimal results in terms of both fairness and accuracy. In this work, we present a new approach for fair representation learning that takes into account the target hypothesis class of models that will be learned from the representation. Specifically, we show how to leverage information about the reproducing kernel Hilbert space (RKHS) to learn a fair representation for kernel-based models with provable fairness and accuracy guarantees. Our approach builds on the classic Sufficient Dimension Reduction (SDR) framework [Li, 1991, Cook 1991, Cook, 1998, Fukumizu et al., 2004, 2009, Wu et al., 2009, Cook and Forzani, 2009]and Weisberg, which is used to compute a low-dimensional projection of the feature vector X that captures all information related to the response Y. Our key insight is that we can instead perform SDR with respect to the protected attributes S, and then take the orthogonal complement of the resulting projection to obtain a fair subspace of the RKHS that captures information in X unrelated to S. We show that functions in the fair subspace 2.2), and we leverage this fact to prove that our approachwill be independent of S under mild conditions (§

Integer-valued and count data are ubiquitous in many fields, including epidemiology (Osthus et al., 2018; Kowal, 2019), ecology (Dorazio et al., 2005), and insurance (Bening and Korolev, 2012), among others (Cameron and Trivedi, 2013). Count data also serve as an indicator of demand, such as the demand for medical services (Deb and Trivedi, 1997), emergency medical services (Matteson et al., 2011), and call center access (Shen and Huang, 2008). In these applications and many others, integer-valued data are frequently observed jointly with predictors, over time intervals, or across spatial locations. Integer-valued data also exhibit a variety of distributional features, including zero-inflation, skewness, over-or underdispersion, and in some cases may be bounded or censored. Flexible and interpretable models for integervalued processes are therefore highly useful in practice. The most widely-used models for count data build upon the Poisson distribution. However, the limitations of the Poisson distribution are well-known: the distribution is not sufficiently flexible in practice and cannot account for zero-inflation or over-and underdispersion. A common strategy is to generalize the Poisson model by introducing additional parameters.

We consider the problem of learning the link parameters as well as the structure of a binary-valued pairwise Markov model. We propose a method based on $l_1$- regularized logistic regression, which estimate globally the whole set of edges and link parameters. Unlike the more recent methods discussed in literature that learn the edges and the corresponding link parameters one node at a time, in this work we propose a method that learns all the edges and corresponding link parameters simultaneously for all nodes, in a global manner. The idea behind this proposal is to exploit the reciprocal information of the nodes between each other during the estimation process. Detailed numerical experiments highlight the advantage of this technique and confirm the intuition behind it.

The phenomenon of benign overfitting is one of the key mysteries uncovered by deep learning methodology: deep neural networks seem to predict well, even with a perfect fit to noisy training data. Motivated by this phenomenon, we consider when a perfect fit to training data in linear regression is compatible with accurate prediction. We give a characterization of gaussian linear regression problems for which the minimum norm interpolating prediction rule has near-optimal prediction accuracy. The characterization is in terms of two notions of the effective rank of the data covariance. It shows that overparameterization is essential for benign overfitting in this setting: the number of directions in parameter space that are unimportant for prediction must significantly exceed the sample size.

The hedonic approach based on a regression model has been widely adopted for the prediction of real estate property price and rent. In particular, a spatial regression technique called Kriging, a method of interpolation that was advanced in the field of spatial statistics, are known to enable high accuracy prediction in light of the spatial dependence of real estate property data. Meanwhile, there has been a rapid increase in machine learning-based prediction using a large (big) dataset and its effectiveness has been demonstrated in previous studies. However, no studies have ever shown the extent to which predictive accuracy differs for Kriging and machine learning techniques using big data. Thus, this study compares the predictive accuracy of apartment rent price in Japan between the nearest neighbor Gaussian processes (NNGP) model, which enables application of Kriging to big data, and the deep neural network (DNN), a representative machine learning technique, with a particular focus on the data sample size (n = 10^4, 10^5, 10^6) and differences in predictive performance. Our analysis showed that, with an increase in sample size, the out-of-sample predictive accuracy of DNN approached that of NNGP and they were nearly equal on the order of n = 10^6. Furthermore, it is suggested that, for both higher and lower end properties whose rent price deviates from the median, DNN may have a higher predictive accuracy than that of NNGP.

Introduced by Breiman (2001), Random Forests (RF) is one of the algorithms of choice in many supervised learning applications. The appeal of these methods comes from their remarkable accuracy in a variety of tasks, the small number (or even the absence) of parameters to tune, their reasonable computational cost at training and prediction time, and their suitability in highdimensional settings. Most commonly used RF algorithms, such as the original random forest procedure (Breiman, 2001), extra-trees (Geurts et al., 2006), or conditional inference forest (Hothorn et al., 2010) are batch algorithms, that require the whole dataset to be available at once. Several online random forests variants have been proposed to overcome this issue and handle data that come sequentially. Utgoff (1989) was the first to extend Quinlan's ID3 batch decision tree algorithm (see Quinlan, 1986) to an online setting. Later on, Domingos and Hulten (2000) introduce Hoeffding Trees that can be easily updated: since observations are available sequentially, a cell is split when (i) enough observations have fallen into this cell, (ii) the best split in the cell is statistically relevant (a generic Hoeffding inequality being used to assess the quality of the best split). Since random forests are known to exhibit better empirical performances than individual decision trees, online random forests have been proposed (see, e.g., Saffari et al., 2009; Denil et al., 2013).

Statistical Learning is the process of estimating an unknown probabilistic input-output relationship of a system using a limited number of observations; and a statistical learning machine (SLM) is the machine that learned such a process. While their roots grow deeply in Probability Theory, SLMs are ubiquitous in the modern world. Automatic Target Recognition (ATR) in military applications, Computer Aided Diagnosis (CAD) in medical imaging, DNA microarrays in Genomics, Optical Character Recognition (OCR), Speech Recognition (SR), spam email filtering, stock market prediction, etc., are few examples and applications for SLM; diverse fields but one theory. The field of Statistical Learning can be decomposed to two basic subfields, Design and Assessment. Three main groups of specializations-namely statisticians, engineers, and computer scientists (ordered ascendingly by programming capabilities and descendingly by mathematical rigor)-exist on the venue of this field and each takes its elephant bite. Exaggerated rigorous analysis of statisticians sometimes deprives them from considering new ML techniques and methods that, yet, have no "complete" mathematical theory. On the other hand, immoderate add-hoc simulations of computer scientists sometimes derive them towards unjustified and immature results. A prudent approach is needed that has the enough flexibility to utilize simulations and trials and errors without sacrificing any rigor. If this prudent attitude is necessary for this field it is necessary, as well, in other fields of Engineering.

The empirical analysis of experiments and quasi-experiments often seeks to determine the optimal allocation of treatments that maximizes social welfare. In the presence of interference, spillover effects lead to a new formulation of the statistical treatment choice problem. This paper develops a novel method to construct individual-specific optimal treatment allocation rules under network interference. Several features make the proposed methodology particularly appealing for applications: we construct targeting rules that depend on an arbitrary set of individual, neighbors' and network characteristics, and we allow for general constraints on the policy function; we consider heterogeneous direct and spillover effects, arbitrary, possibly non-linear, regression models, and we propose estimators that are robust to model misspecification; the method flexibly accommodates for cases where researchers only observe local information of the network. From a theoretical perspective, we establish the first set of guarantees on the utilitarian regret under interference, and we show that it achieves the min-max optimal rate in scenarios of practical and theoretical interest. We discuss the empirical performance in simulations and we illustrate our method by investigating the role of social networks in micro-finance decisions.

Stacking methods improve the prediction performance of regression models. A simple way to stack base regressions estimators is by combining them linearly, as done by \citet{breiman1996stacked}. Even though this approach is useful from an interpretative perspective, it often does not lead to high predictive power. We propose the NN-Stacking method (NNS), which generalizes Breiman's method by allowing the linear parameters to vary with input features. This improvement enables NNS to take advantage of the fact that distinct base models often perform better at different regions of the feature space. Our method uses neural networks to estimate the stacking coefficients. We show that while our approach keeps the interpretative features of Breiman's method at a local level, it leads to better predictive power, especially in datasets with large sample sizes.

In this paper, we apply machine learning to distributed private data owned by multiple data owners, entities with access to non-overlapping training datasets. We use noisy, differentially-private gradients to minimize the fitness cost of the machine learning model using stochastic gradient descent. We quantify the quality of the trained model, using the fitness cost, as a function of privacy budget and size of the distributed datasets to capture the trade-off between privacy and utility in machine learning. This way, we can predict the outcome of collaboration among privacy-aware data owners prior to executing potentially computationally-expensive machine learning algorithms. Particularly, we show that the difference between the fitness of the trained machine learning model using differentially-private gradient queries and the fitness of the trained machine model in the absence of any privacy concerns is inversely proportional to the size of the training datasets squared and the privacy budget squared. We successfully validate the performance prediction with the actual performance of the proposed privacy-aware learning algorithms, applied to: financial datasets for determining interest rates of loans using regression; and detecting credit card frauds using support vector machines.