We provide an adversarial approach to estimating Riesz representers of linear functionals within arbitrary function spaces. We prove oracle inequalities based on the localized Rademacher complexity of the function space used to approximate the Riesz representer and the approximation error. These inequalities imply fast finite sample mean-squared-error rates for many function spaces of interest, such as high-dimensional sparse linear functions, neural networks and reproducing kernel Hilbert spaces. Our approach offers a new way of estimating Riesz representers with a plethora of recently introduced machine learning techniques. We show how our estimator can be used in the context of de-biasing structural/causal parameters in semi-parametric models, for automated orthogonalization of moment equations and for estimating the stochastic discount factor in the context of asset pricing.

The effect of training data size on machine learning methods has been well investigated over the past two decades. The predictive performance of tree based machine learning methods, in general, improves with a decreasing rate as the size of training data increases. We investigate this in optimal trees ensemble (OTE) where the method fails to learn from some of the training observations due to internal validation. Modified tree selection methods are thus proposed for OTE to cater for the loss of training observations in internal validation. In the first method, corresponding out-of-bag (OOB) observations are used in both individual and collective performance assessment for each tree. Trees are ranked based on their individual performance on the OOB observations. A certain number of top ranked trees is selected and starting from the most accurate tree, subsequent trees are added one by one and their impact is recorded by using the OOB observations left out from the bootstrap sample taken for the tree being added. A tree is selected if it improves predictive accuracy of the ensemble. In the second approach, trees are grown on random subsets, taken without replacement-known as sub-bagging, of the training data instead of bootstrap samples (taken with replacement). The remaining observations from each sample are used in both individual and collective assessments for each corresponding tree similar to the first method. Analysis on 21 benchmark datasets and simulations studies show improved performance of the modified methods in comparison to OTE and other state-of-the-art methods.

One of the main goals of statistical modelling is to understand the dependence of a response variable, Y, with respect to another explanatory variable, X. This type of dependence can be studied through nonparametric regression models, where the relationship between Y and X is modelled without specifying in advance the function that links them. Within this framework, the study of the regression curves can be useful in the comparison of two or more groups, which is an important problem associated with statistical inference. In particular, the topic of hypothesis testing the equality of mean functions has been widely investigated in the literature, see, for instance, the review that González-Manteiga and Crujeiras (2013) offers about this topic. Relevant papers on this topic are Hall and Hart (1990); King et al. (1991); Delgado (1993); Kulasekera (1995); Young and Bowman (1995); Dette and Neumeyer (2001); Pardo-Fernández et al. (2007); Srihera and Stute (2010), among others. Furthermore, in order to compare the values of a response variable across several groups in the presence of a covariate effect, nonparametric analysis of covariance or factor-by-curve interaction test can be used. Young and Bowman (1995) generalized the one-way analysis of variance test to the nonparametric regression setting, and Dette and Neumeyer (2001) proposed to use Young and Bowman's test also in the situation of a heteroscedastic error. In addition, Park and Kang (2008) developed a SiZer tool based on an analysis of variance type test statistic that is capable of comparing multiple curves based on the residuals. The evolution of this procedure is based on the comparison using the original regression curves (Park et al., 2014).

Training a classifier under fairness constraints has gotten increasing attention in the machine learning community thanks to moral, legal, and business reasons. However, several recent works addressing algorithmic fairness have only focused on simple models such as logistic regression or support vector machines due to non-convex and non-differentiable fairness criteria across protected groups, such as race or gender. Neural networks, the most widely used models for classification nowadays, are precluded and lack theoretical guarantees. This paper aims to fill this missing but crucial part of the literature of algorithmic fairness for neural networks. In particular, we show that overparametrized neural networks could meet the fairness constraints. The key ingredient of building a fair neural network classifier is establishing no-regret analysis for neural networks in the overparameterization regime, which may be of independent interest in the online learning of neural networks and related applications.

As machine learning algorithms grow in popularity and diversify to many industries, ethical and legal concerns regarding their fairness have become increasingly relevant. We explore the problem of algorithmic fairness, taking an information-theoretic view. The maximal correlation framework is introduced for expressing fairness constraints and shown to be capable of being used to derive regularizers that enforce independence and separation-based fairness criteria, which admit optimization algorithms for both discrete and continuous variables which are more computationally efficient than existing algorithms. We show that these algorithms provide smooth performance-fairness tradeoff curves and perform competitively with state-of-the-art methods on both discrete datasets (COMPAS, Adult) and continuous datasets (Communities and Crimes).

Despite the enormous amount of data, particular events of interest can still be quite rare. Classification of rare events is a common problem in many domains, such as fraudulent transactions, malware traffic analysis and network intrusion detection. Many studies have been developed for malware detection using machine learning approaches on various datasets, but as far as we know only the MTA-KDD'19 dataset has the peculiarity of updating the representative set of malicious traffic on a daily basis. This daily updating is the added value of the dataset, but it translates into a potential due to the class imbalance problem that the RRw-Optimized MTA-KDD'19 will occur. We capture difficulties of class distribution in real datasets by considering four types of minority class examples: safe, borderline, rare and outliers. In this work, we developed two versions of Generative Silhouette Resampling 1-Nearest Neighbour (G1Nos) oversampling algorithms for dealing with class imbalance problem. The first module of G1Nos algorithms performs a coefficient-based instance selection silhouette identifying the critical threshold of Imbalance Degree. (ID), the second module generates synthetic samples using a SMOTE-like oversampling algorithm. The balancing of the classes is done by our G1Nos algorithms to re-establish the proportions between the two classes of the used dataset. The experimental results show that our oversampling algorithm work better than the other two SOTA methodologies in all the metrics considered.

Operational Processes are defined as the core business of companies and firms: drug companies consider them to be drug testing and approval, manufacturing firms identify them in the product assembly process, while banks and financial firms have their own core business in risk management and evaluation. In order to be able to concede loans, financial institutions are compelled to predict whether an applicant is likely to repay the debit. In such a framework, Credit Scoring plays a huge role in ranking applicants based on their likelihood to pay back the loan. Each person is associated with a credit score value, namely a "number that summarizes its credit risk, based on a snapshot of its credit report at a particular point in time" [1]. Behind the scenes, CRM is employed to reach the goal: scoring models, or "scorecards", are generated from historical data, employing well-established statistical techniques. The cornerstones of a reliable scorecard are well depicted by Loretta Mester in [2]: "the model should give a higher percentage of high scores to borrowers whose loans will perform well and a higher percentage of low scores to borrowers whose loans won't perform well". Several advantages stem from risk modelling, among the most important there are an increased profitability of financial corporations due to more reliable loans conceded, the chance of evaluating new loan programs based on the data collected and the enhancement of the credit-loss management capability [1]. Therefore, over the years, some institutions arose to accomplish the task. CRIF is a global company specialized in credit bureau and business information, outsourcing and processing services, and credit solutions.

With large quantities of data typically available nowadays, forecasting models that are trained across sets of time series, known as Global Forecasting Models (GFM), are regularly outperforming traditional univariate forecasting models that work on isolated series. As GFMs usually share the same set of parameters across all time series, they often have the problem of not being localised enough to a particular series, especially in situations where datasets are heterogeneous. We study how ensembling techniques can be used with generic GFMs and univariate models to solve this issue. Our work systematises and compares relevant current approaches, namely clustering series and training separate submodels per cluster, the so-called ensemble of specialists approach, and building heterogeneous ensembles of global and local models. We fill some gaps in the approaches and generalise them to different underlying GFM model types. We then propose a new methodology of clustered ensembles where we train multiple GFMs on different clusters of series, obtained by changing the number of clusters and cluster seeds. Using Feed-forward Neural Networks, Recurrent Neural Networks, and Pooled Regression models as the underlying GFMs, in our evaluation on six publicly available datasets, the proposed models are able to achieve significantly higher accuracy than baseline GFM models and univariate forecasting methods.

We propose a goodness-of-fit test for degree-corrected stochastic block models (DCSBM). The test is based on an adjusted chi-square statistic for measuring equality of means among groups of $n$ multinomial distributions with $d_1,\dots,d_n$ observations. In the context of network models, the number of multinomials, $n$, grows much faster than the number of observations, $d_i$, hence the setting deviates from classical asymptotics. We show that a simple adjustment allows the statistic to converge in distribution, under null, as long as the harmonic mean of $\{d_i\}$ grows to infinity. This result applies to large sparse networks where the role of $d_i$ is played by the degree of node $i$. Our distributional results are nonasymptotic, with explicit constants, providing finite-sample bounds on the Kolmogorov-Smirnov distance to the target distribution. When applied sequentially, the test can also be used to determine the number of communities. The test operates on a (row) compressed version of the adjacency matrix, conditional on the degrees, and as a result is highly scalable to large sparse networks. We incorporate a novel idea of compressing the columns based on a $(K+1)$-community assignment when testing for $K$ communities. This approach increases the power in sequential applications without sacrificing computational efficiency, and we prove its consistency in recovering the number of communities. Since the test statistic does not rely on a specific alternative, its utility goes beyond sequential testing and can be used to simultaneously test against a wide range of alternatives outside the DCSBM family. We show the effectiveness of the approach by extensive numerical experiments with simulated and real data. In particular, applying the test to the Facebook-100 dataset, we find that a DCSBM with a small number of communities is far from a good fit in almost all cases.

Prediction models are often employed in estimating parameters of optimization models. Despite the fact that in an end-to-end view, the real goal is to achieve good optimization performance, the prediction performance is measured on its own. While it is usually believed that good prediction performance in estimating the parameters will result in good subsequent optimization performance, formal theoretical guarantees on this are notably lacking. In this paper, we explore conditions that allow us to explicitly describe how the prediction performance governs the optimization performance. Our weaker condition allows for an asymptotic convergence result, while our stronger condition allows for exact quantification of the optimization performance in terms of the prediction performance. In general, verification of these conditions is a non-trivial task. Nevertheless, we show that our weaker condition is equivalent to the well-known Fisher consistency concept from the learning theory literature. This then allows us to easily check our weaker condition for several loss functions. We also establish that the squared error loss function satisfies our stronger condition. Consequently, we derive the exact theoretical relationship between prediction performance measured with the squared loss, as well as a class of symmetric loss functions, and the subsequent optimization performance. In a computational study on portfolio optimization, fractional knapsack and multiclass classification problems, we compare the optimization performance of using of several prediction loss functions (some that are Fisher consistent and some that are not) and demonstrate that lack of consistency of the loss function can indeed have a detrimental effect on performance.