Statistical analysis is increasingly confronted with complex data from general metric spaces, such as symmetric positive definite matrix-valued data and probability distribution functions. [47] and [17] establish a general paradigm of Fr\'echet regression with complex metric space valued responses and Euclidean predictors. However, their proposed local Fr\'echet regression approach involves nonparametric kernel smoothing and suffers from the curse of dimensionality. To address this issue, we in this paper propose a novel random forests weighted local Fr\'echet regression paradigm. The main mechanism of our approach relies on the adaptive kernels generated by random forests. Our first method utilizes these weights as the local average to solve the Fr\'echet mean, while the second method performs local linear Fr\'echet regression, making both methods locally adaptive. Our proposals significantly improve existing Fr\'echet regression methods. Based on the theory of infinite order U-processes and infinite order Mmn-estimator, we establish the consistency, rate of convergence, and asymptotic normality for our proposed random forests weighted Fr\'echet regression estimator, which covers the current large sample theory of random forests with Euclidean responses as a special case. Numerical studies show the superiority of our proposed two methods for Fr\'echet regression with several commonly encountered types of responses such as probability distribution functions, symmetric positive definite matrices, and sphere data. The practical merits of our proposals are also demonstrated through the application to the human mortality distribution data.

In this paper we present a novel agent-based modeling methodology to predict rooftop solar adoptions in the residential energy market. We first applied several linear regression models to estimate missing variables for non-adopters, so that attributes of non-adopters and adopters could be used to train a logistic regression model. Then, we integrated the logistic regression model along with other predictive models into a multi-agent simulation platform and validated our models by comparing the forecast of aggregate adoptions in a typical zip code area with its ground truth. This result shows that the agent-based model can reliably predict future adoptions. Finally, based on the validated agent-based model, we compared the outcome of a hypothesized seeding policy with the original incentive plan, and investigated other alternative seeding policies which could lead to more adopters.

Privacy policies are commonly used to inform users about the data collection and use practices of websites, mobile apps, and other products and services. However, the average Internet user struggles to understand the contents of these documents and generally does not read them. Natural language and machine learning techniques offer the promise of automatically extracting relevant statements from privacy policies to help generate succinct summaries, but current techniques require large amounts of annotated data. The highest quality annotations require law experts, but their efforts do not scale efficiently. In this paper, we present results on bridging the gap between privacy practice categories defined by law experts with topics learned from Non-negative Matrix Factorization (NMF). To do this, we investigate the intersections between vocabulary sets identified as most significant for each category, using a logistic regression model, and vocabulary sets identified by topic modeling. The intersections exhibit strong matches between some categories and topics, although other categories have weaker affinities with topics. Our results show a path forward for applying unsupervised methods to the determination of data practice categories in privacy policy text.

Speech acts are a way to conceptualize speech as action. This holds true for communication on any platform, including social media platforms such as Twitter.

In the recent years, reciprocal link prediction has received some attention from the data mining and social network analysis researchers, who solved this problem as a binary classification task. However, it is also important to predict the interval time for the creation of reciprocal link. This is a challenging problem for two reasons: First, the lack of effective features, because well-known link prediction features are designed for undirected networks and for the binary classification task, hence they do not work well for the interval time prediction; Second, the presence of censored data instances makes the traditional supervised regression methods unsuitable for solving this problem. In this paper, we propose a solution for the reciprocal link interval time prediction task. We map this problem into survival analysis framework and show through extensive experiments on real-world datasets that, survival analysis methods perform better than traditional regression, neural network based model and support vector regression (SVR).

Accurate predictions about future events is essential in many areas, one of them being the Tourism Industry. Usually, countries and cities invest a huge amount of money in planning and preparation in order to welcome (and profit from) tourists. An accurate prediction of the number of visits in the following days or months could help both the economy and tourists. Prior studies in this domain explore forecasting for a whole country rather than for fine-grained areas within a country (e.g., specific touristic attractions). In this work, we suggest that accessible data from online social networks and travel websites, in addition to climate data, can be used to support the inference of visitation count for many touristic attractions. To test our hypothesis we analyze visitation, climate and social media data in more than 70 National Parks in U.S during the last 3 years. The experimental results reveal a high correlation between social media data and tourism demands; in fact, in over 80\% of the parks, social media reviews and visitation counts are correlated by more than 50\%. Moreover, we assess the effectiveness of employing various prediction techniques, finding that even a simple linear regression model, when fed with social media and climate data as input features, can attain a prediction accuracy of over 80\% while a more robust algorithm, such as Support Vector Regression, reaches up to 94\% accuracy.

Machine Learning has attracted considerable attention throughout the past decade due to its potential to solve far-reaching tasks, such as image classification, object recognition, anomaly detection, and data forecasting. A standard approach to tackle such applications is based on supervised learning, which is assisted by large sets of labeled data and is conducted by the so-called classifiers, such as Logistic Regression, Decision Trees, Random Forests, and Support Vector Machines, among others. An alternative to traditional classifiers is the parameterless Optimum-Path Forest (OPF), which uses a graph-based methodology and a distance measure to create arcs between nodes and hence sets of trees, responsible for conquering the nodes, defining their labels, and shaping the forests. Nevertheless, its performance is strongly associated with an appropriate distance measure, which may vary according to the dataset's nature. Therefore, this work proposes a comparative study over a wide range of distance measures applied to the supervised Optimum-Path Forest classification. The experimental results are conducted using well-known literature datasets and compared across benchmarking classifiers, illustrating OPF's ability to adapt to distinct domains.

Optimization of real-world black-box functions defined over purely categorical variables is an active area of research. In particular, optimization and design of biological sequences with specific functional or structural properties have a profound impact in medicine, materials science, and biotechnology. Standalone search algorithms, such as simulated annealing (SA) and Monte Carlo tree search (MCTS), are typically used for such optimization problems. In order to improve the performance and sample efficiency of such algorithms, we propose to use existing methods in conjunction with a surrogate model for the black-box evaluations over purely categorical variables. To this end, we present two different representations, a group-theoretic Fourier expansion and an abridged one-hot encoded Boolean Fourier expansion. To learn such representations, we consider two different settings to update our surrogate model. First, we utilize an adversarial online regression setting where Fourier characters of each representation are considered as experts and their respective coefficients are updated via an exponential weight update rule each time the black box is evaluated. Second, we consider a Bayesian setting where queries are selected via Thompson sampling and the posterior is updated via a sparse Bayesian regression model (over our proposed representation) with a regularized horseshoe prior. Numerical experiments over synthetic benchmarks as well as real-world RNA sequence optimization and design problems demonstrate the representational power of the proposed methods, which achieve competitive or superior performance compared to state-of-the-art counterparts, while improving the computation cost and/or sample efficiency, substantially.

The problem of learning functions over spaces of probabilities - or distribution regression - is gaining significant interest in the machine learning community. A key challenge behind this problem is to identify a suitable representation capturing all relevant properties of the underlying functional mapping. A principled approach to distribution regression is provided by kernel mean embeddings, which lifts kernel-induced similarity on the input domain at the probability level. This strategy effectively tackles the two-stage sampling nature of the problem, enabling one to derive estimators with strong statistical guarantees, such as universal consistency and excess risk bounds. However, kernel mean embeddings implicitly hinge on the maximum mean discrepancy (MMD), a metric on probabilities, which may fail to capture key geometrical relations between distributions. In contrast, optimal transport (OT) metrics, are potentially more appealing, as documented by the recent literature on the topic. In this work, we propose the first OT-based estimator for distribution regression. We build on the Sliced Wasserstein distance to obtain an OT-based representation. We study the theoretical properties of a kernel ridge regression estimator based on such representation, for which we prove universal consistency and excess risk bounds. Preliminary experiments complement our theoretical findings by showing the effectiveness of the proposed approach and compare it with MMD-based estimators.

Much of the past work on fairness in machine learning has focused on forcing the predictions of classifiers to have similar statistical properties for individuals of different demographics. Yet, such methods often simply perform a rescaling of the classifier scores and ignore whether individuals of different groups have similar features. Our proposed method, Optimal Transport to Fairness (OTF), applies Optimal Transport (OT) to take this similarity into account by quantifying unfairness as the smallest cost of OT between a classifier and any score function that satisfies fairness constraints. For a flexible class of linear fairness constraints, we show a practical way to compute OTF as an unfairness cost term that can be added to any standard classification setting. Experiments show that OTF can be used to achieve an effective trade-off between predictive power and fairness.