We consider the statistical analysis of heterogeneous data for clustering and prediction purposes, in situations where the observations include functions, typically time series. We extend the modeling with Mixtures-of-Experts (ME), as a framework of choice in modeling heterogeneity in data for prediction and clustering with vectorial observations, to this functional data analysis context. We first present a new family of functional ME (FME) models, in which the predictors are potentially noisy observations, from entire functions, and the data generating process of the pair predictor and the real response, is governed by a hidden discrete variable representing an unknown partition, leading to complex situations to which the standard ME framework is not adapted. Second, we provide sparse and interpretable functional representations of the FME models, thanks to Lasso-like regularizations, notably on the derivatives of the underlying functional parameters of the model, projected onto a set of continuous basis functions. We develop dedicated expectation--maximization algorithms for Lasso-like regularized maximum-likelihood parameter estimation strategies, to encourage sparse and interpretable solutions. The proposed FME models and the developed EM-Lasso algorithms are studied in simulated scenarios and in applications to two real data sets, and the obtained results demonstrate their performance in accurately capturing complex nonlinear relationships between the response and the functional predictor, and in clustering.

Recent research has found that neural networks are vulnerable to several types of adversarial attacks, where the input samples are modified in such a way that the model produces a wrong prediction that misclassifies the adversarial sample. In this paper we focus on black-box adversarial attacks, that can be performed without knowing the inner structure of the attacked model, nor the training procedure, and we propose a novel attack that is capable of correctly attacking a high percentage of samples by rearranging a small number of pixels within the attacked image. We demonstrate that our attack works on a large number of datasets and models, that it requires a small number of iterations, and that the distance between the original sample and the adversarial one is negligible to the human eye.

Causal inference is essential for data-driven decision making across domains such as business engagement, medical treatment or policy making. However, research on causal discovery and inference has evolved separately, and the combination of the two domains is not trivial. In this work, we develop Deep End-to-end Causal Inference (DECI), a single flow-based method that takes in observational data and can perform both causal discovery and inference, including conditional average treatment effect (CATE) estimation. We provide a theoretical guarantee that DECI can recover the ground truth causal graph under mild assumptions. In addition, our method can handle heterogeneous, real-world, mixed-type data with missing values, allowing for both continuous and discrete treatment decisions. Moreover, the design principle of our method can generalize beyond DECI, providing a general End-to-end Causal Inference (ECI) recipe, which enables different ECI frameworks to be built using existing methods. Our results show the superior performance of DECI when compared to relevant baselines for both causal discovery and (C)ATE estimation in over a thousand experiments on both synthetic datasets and other causal machine learning benchmark datasets.

We propose a method to distinguish causal influence from hidden confounding in the following scenario: given a target variable Y, potential causal drivers X, and a large number of background features, we propose a novel criterion for identifying causal relationship based on the stability of regression coefficients of X on Y with respect to selecting different background features. To this end, we propose a statistic V measuring the coefficient's variability. We prove, subject to a symmetry assumption for the background influence, that V converges to zero if and only if X contains no causal drivers. In experiments with simulated data, the method outperforms state of the art algorithms. Further, we report encouraging results for real-world data. Our approach aligns with the general belief that causal insights admit better generalization of statistical associations across environments, and justifies similar existing heuristic approaches from the literature.

Community resilience in the face of natural hazards relies on a community's potential to bounce back. A failure to integrate equity into resilience considerations results in unequal recovery and disproportionate impacts on vulnerable populations, which has long been a concern in the United States. This research investigated aspects of equity related to community resilience in the aftermath of Winter Storm Uri in Texas which led to extended power outages for more than 4 million households. County level outage and recovery data was analyzed to explore potential significant links between various county attributes and their share of the outages during the recovery and restoration phases. Next, satellite imagery was used to examine data at a much higher geographical resolution focusing on census tracts in the city of Houston. The goal was to use computer vision to extract the extent of outages within census tracts and investigate their linkages to census tracts attributes. Results from various statistical procedures revealed statistically significant negative associations between counties' percentage of non-Hispanic whites and median household income with the ratio of outages. Additionally, at census tract level, variables including percentages of linguistically isolated population and public transport users exhibited positive associations with the group of census tracts that were affected by the outage as detected by computer vision analysis. Informed by these results, engineering solutions such as the applicability of grid modernization technologies, together with distributed and renewable energy resources, when controlled for the region's topographical characteristics, are proposed to enhance equitable power grid resiliency in the face of natural hazards.

This article was published as a part of the Data Science Blogathon. For this article, we will be using sklearn's make_classification dataset with four features This is the vectorised form of the gradient descent expression, which we will be using in our code. Now that we are done with every part, we will put everything together in a single class. You can fiddle around with hyper-parameters and see the behaviour of cost function. Now, let's see how our logistic regression fares in comparison to sklearn's logistic regression.

Data Science and Machine Learning are the hottest skills in demand but challenging to learn. Did you wish that there was one course for Data Science and Machine Learning that covers everything from Math for Machine Learning, Advance Statistics for Data Science, Data Processing, Machine Learning A-Z, Deep learning and more? Well, you have come to the right place. This Data Science and Machine Learning course has 11 projects, 250 lectures, more than 25 hours of content, one Kaggle competition project with top 1 percentile score, code templates and various quizzes. Today Data Science and Machine Learning is used in almost all the industries, including automobile, banking, healthcare, media, telecom and others.

SVM stands for support vector machine, and although it can solve both classification and regression problems, it is mainly used for classification problems in machine learning (ML). SVM models help us classify new data points based on previously classified similar data, making it is a supervised machine learning technique. The companion resources to this article can be found either on Google Colab or Github. Classification is a supervised ML task that requires machine learning algorithms that learn how to assign a class label to examples from a problem domain. An easy-to-understand example is classifying emails as "junk" or "not junk."

Time series forecasting is fundamental for various use cases in different domains such as energy systems and economics. Creating a forecasting model for a specific use case requires an iterative and complex design process. The typical design process includes the five sections (1) data pre-processing, (2) feature engineering, (3) hyperparameter optimization, (4) forecasting method selection, and (5) forecast ensembling, which are commonly organized in a pipeline structure. One promising approach to handle the ever-growing demand for time series forecasts is automating this design process. The present paper, thus, analyzes the existing literature on automated time series forecasting pipelines to investigate how to automate the design process of forecasting models. Thereby, we consider both Automated Machine Learning (AutoML) and automated statistical forecasting methods in a single forecasting pipeline. For this purpose, we firstly present and compare the proposed automation methods for each pipeline section. Secondly, we analyze the automation methods regarding their interaction, combination, and coverage of the five pipeline sections. For both, we discuss the literature, identify problems, give recommendations, and suggest future research. This review reveals that the majority of papers only cover two or three of the five pipeline sections. We conclude that future research has to holistically consider the automation of the forecasting pipeline to enable the large-scale application of time series forecasting.

Energy-Based Models (EBMs) have proven to be a highly effective approach for modelling densities on finite-dimensional spaces. Their ability to incorporate domain-specific choices and constraints into the structure of the model through composition make EBMs an appealing candidate for applications in physics, biology and computer vision and various other fields. In this work, we present a novel class of EBM which is able to learn distributions of functions (such as curves or surfaces) from functional samples evaluated at finitely many points. Two unique challenges arise in the functional context. Firstly, training data is often not evaluated along a fixed set of points. Secondly, steps must be taken to control the behaviour of the model between evaluation points, to mitigate overfitting. The proposed infinite-dimensional EBM employs a latent Gaussian process, which is weighted spectrally by an energy function parameterised with a neural network. The resulting EBM has the ability to utilize irregularly sampled training data and can output predictions at any resolution, providing an effective approach to up-scaling functional data. We demonstrate the efficacy of our proposed approach for modelling a range of datasets, including data collected from Standard and Poor's 500 (S\&P) and UK National grid.