Geographic Information Systems (GIS) and related technologies have generated substantial interest among statisticians with regard to scalable methodologies for analyzing large spatial datasets. A variety of scalable spatial process models have been proposed that can be easily embedded within a hierarchical modeling framework to carry out Bayesian inference. While the focus of statistical research has mostly been directed toward innovative and more complex model development, relatively limited attention has been accorded to approaches for easily implementable scalable hierarchical models for the practicing scientist or spatial analyst. This article discusses how point-referenced spatial process models can be cast as a conjugate Bayesian linear regression that can rapidly deliver inference on spatial processes. The approach allows exact sampling directly (avoids iterative algorithms such as Markov chain Monte Carlo) from the joint posterior distribution of regression parameters, the latent process and the predictive random variables, and can be easily implemented on statistical programming environments such as R.

Principal component analysis (PCA) is a well-known linear dimension-reduction method that has been widely used in data analysis and modeling. It is an unsupervised learning technique that identifies a suitable linear subspace for the input variable that contains maximal variation and preserves as much information as possible. PCA has also been used in prediction models where the original, high-dimensional space of predictors is reduced to a smaller, more manageable, set before conducting regression analysis. However, this approach does not incorporate information in the response during the dimension-reduction stage and hence can have poor predictive performance. To address this concern, several supervised linear dimension-reduction techniques have been proposed in the literature. This paper reviews selected techniques, extends some of them, and compares their performance through simulations. Two of these techniques, partial least squares (PLS) and least-squares PCA (LSPCA), consistently outperform the others in this study.

Representation learning constructs low-dimensional representations to summarize essential features of high-dimensional data. This learning problem is often approached by describing various desiderata associated with learned representations; e.g., that they be non-spurious, efficient, or disentangled. It can be challenging, however, to turn these intuitive desiderata into formal criteria that can be measured and enhanced based on observed data. In this paper, we take a causal perspective on representation learning, formalizing non-spuriousness and efficiency (in supervised representation learning) and disentanglement (in unsupervised representation learning) using counterfactual quantities and observable consequences of causal assertions. This yields computable metrics that can be used to assess the degree to which representations satisfy the desiderata of interest and learn non-spurious and disentangled representations from single observational datasets.

Stochastic processes are random variables with values in some space of paths. However, reducing a stochastic process to a path-valued random variable ignores its filtration, i.e. the flow of information carried by the process through time. By conditioning the process on its filtration, we introduce a family of higher order kernel mean embeddings (KMEs) that generalizes the notion of KME and captures additional information related to the filtration. We derive empirical estimators for the associated higher order maximum mean discrepancies (MMDs) and prove consistency. We then construct a filtration-sensitive kernel two-sample test able to pick up information that gets missed by the standard MMD test. In addition, leveraging our higher order MMDs we construct a family of universal kernels on stochastic processes that allows to solve real-world calibration and optimal stopping problems in quantitative finance (such as the pricing of American options) via classical kernel-based regression methods. Finally, adapting existing tests for conditional independence to the case of stochastic processes, we design a causal-discovery algorithm to recover the causal graph of structural dependencies among interacting bodies solely from observations of their multidimensional trajectories.

Machine learning is one of the most trending topics at present and is expected to grow exponentially over the coming years. Before we drill down to one of the most common techniques in machine learning that is the'linear regression', let's understand what exactly is regression. Regression analysis is a form of a predictive modelling technique that establishes a relationship between two variables namely a dependent variable and independent variable. In simpler words, a regression analysis involves graphing a line over a set of data points that most closely fits the overall shape of the data or it can be said that a regression shows the changes in a dependent variable on the y-axis to the change in the explanatory variable on the x-axis. Linear regression aims to establish a linear relationship between two variables where one is the independent variable and other is the dependent variable using a linear equation on the data that is put under observation. For example if we consider the weight and height of a person, as the height increases the weight also increases, hence a linear relationship can be established between the height and weight of a person.

Crop yield prediction is crucial for global food security yet notoriously challenging due to multitudinous factors that jointly determine the yield, including genotype, environment, management, and their complex interactions. Integrating the power of optimization, machine learning, and agronomic insight, we present a new predictive model (referred to as the interaction regression model) for crop yield prediction, which has three salient properties. First, it achieved a relative root mean square error of 8% or less in three Midwest states (Illinois, Indiana, and Iowa) in the US for both corn and soybean yield prediction, outperforming state-of-the-art machine learning algorithms. Second, it identified about a dozen environment by management interactions for corn and soybean yield, some of which are consistent with conventional agronomic knowledge whereas some others interactions require additional analysis or experiment to prove or disprove. Third, it quantitatively dissected crop yield into contributions from weather, soil, management, and their interactions, allowing agronomists to pinpoint the factors that favorably or unfavorably affect the yield of a given location under a given weather and management scenario. The most significant contribution of the new prediction model is its capability to produce accurate prediction and explainable insights simultaneously. This was achieved by training the algorithm to select features and interactions that are spatially and temporally robust to balance prediction accuracy for the training data and generalizability to the test data.

Word embeddings are a powerful natural lan-guage processing technique, but they are ex-tremely difficult to interpret. To enable inter-pretable NLP models, we create vectors whereeach dimension isinherently interpretable. Byinherently interpretable, we mean a systemwhere each dimension is associated with somehuman-understandablehintthat can describethe meaning of that dimension. In order tocreate more interpretable word embeddings,we transform pretrained dense word embed-dings into sparse embeddings. These new em-beddings are inherently interpretable: each oftheir dimensions is created from and repre-sents a natural language word or specific gram-matical concept. We construct these embed-dings through sparse coding, where each vec-tor in the basis set is itself a word embedding.Therefore, each dimension of our sparse vec-tors corresponds to a natural language word.We also show that models trained using thesesparse embeddings can achieve good perfor-mance and are more interpretable in practice,including through human evaluations.

Recapping the primary step when conducting a model analysis, it is always important to import libraries and modules to access specific features. The standard imports are added, such as Matplotlib, pandas, NumPy and seaborn, as well as sklearn which allows us to split our sets into testing and training sets, along with the preprocessing of our data. On the 7th and 8th lines, we integrate TensorFlow with Keras. Keras is a high-level API of TensorFlow, so we must import them this way. The data being explored is a set consisting of patients' tumour data. Depending on the tumour size, our data will tell us if the patient is susceptible to cancer or not. Below is the data of the first 10 patients in the dataset. There are 101 patients in total.

This paper presents the contribution of the Data Science Kitchen at GermEval 2021 shared task on the identification of toxic, engaging, and fact-claiming comments. The task aims at extending the identification of offensive language, by including additional subtasks that identify comments which should be prioritized for fact-checking by moderators and community managers. Our contribution focuses on a feature-engineering approach with a conventional classification backend. We combine semantic and writing style embeddings derived from pre-trained deep neural networks with additional numerical features, specifically designed for this task. Ensembles of Logistic Regression classifiers and Support Vector Machines are used to derive predictions for each subtask via a majority voting scheme. Our best submission achieved macro-averaged F1-scores of 66.8%, 69.9% and 72.5% for the identification of toxic, engaging, and fact-claiming comments.

Recent development in data-driven decision science has seen great advances in individualized decision making. Given data with individual covariates, treatment assignments and outcomes, researchers can search for the optimal individualized treatment rule (ITR) that maximizes the expected outcome. Existing methods typically require initial estimation of some nuisance models. The double robustness property that can protect from misspecification of either the treatment-free effect or the propensity score has been widely advocated. However, when model misspecification exists, a doubly robust estimate can be consistent but may suffer from downgraded efficiency. Other than potential misspecified nuisance models, most existing methods do not account for the potential problem when the variance of outcome is heterogeneous among covariates and treatment. We observe that such heteroscedasticity can greatly affect the estimation efficiency of the optimal ITR. In this paper, we demonstrate that the consequences of misspecified treatment-free effect and heteroscedasticity can be unified as a covariate-treatment dependent variance of residuals. To improve efficiency of the estimated ITR, we propose an Efficient Learning (E-Learning) framework for finding an optimal ITR in the multi-armed treatment setting. We show that the proposed E-Learning is optimal among a regular class of semiparametric estimates that can allow treatment-free effect misspecification. In our simulation study, E-Learning demonstrates its effectiveness if one of or both misspecified treatment-free effect and heteroscedasticity exist. Our analysis of a Type 2 Diabetes Mellitus (T2DM) observational study also suggests the improved efficiency of E-Learning.