In this article, I am going to share a few machine learning work I have done in spark using PySpark. Machine Learning is one of the hot application of artificial intelligence (AI). AI is a much bigger ecosystem with many amazing applications. Machine learning in simple terms is the ability to automatically learn by the machine and improve from experience without explicitly programmed. The learning process starts with observation of data, then it finds the pattern in date and makes a better decision on learning from data.

As we know, 'Data is the new oil.' It means that just like oil. If one knows the value of data, we can learn to extract and use, it can solve many problems. Now, data can be explained by two things, Model and Error. In this article, we are going to dive into the linear model.

In this article, we will be exploring various feature selection techniques that we need to be familiar with, in order to get the best performance out of your model. SelectKbest is a method provided by sklearn to rank features of a dataset by their "importance "with respect to the target variable. This "importance" is calculated using a score function which can be one of the following: All of the above-mentioned scoring functions are based on statistics. For instance, the f_regression function arranges the p_values of each of the variables in increasing order and picks the best K columns with the least p_value. Features with a p_value of less than 0.05 are considered "significant" and only these features should be used in the predictive model.

In recent years, bankruptcy forecasting has gained lot of attention from researchers as well as practitioners in the field of financial risk management. For bankruptcy prediction, various approaches proposed in the past and currently in practice relies on accounting ratios and using statistical modeling or machine learning methods. These models have had varying degrees of successes. Models such as Linear Discriminant Analysis or Artificial Neural Network employ discriminative classification techniques. They lack explicit provision to include prior expert knowledge. In this paper, we propose another route of generative modeling using Expert Bayesian framework. The biggest advantage of the proposed framework is an explicit inclusion of expert judgment in the modeling process. Also the proposed methodology provides a way to quantify uncertainty in prediction. As a result the model built using Bayesian framework is highly flexible, interpretable and intuitive in nature. The proposed approach is well suited for highly regulated or safety critical applications such as in finance or in medical diagnosis. In such cases accuracy in the prediction is not the only concern for decision makers. Decision makers and other stakeholders are also interested in uncertainty in the prediction as well as interpretability of the model. We empirically demonstrate these benefits of proposed framework on real world dataset using Stan, a probabilistic programming language. We found that the proposed model is either comparable or superior to the other existing methods. Also resulting model has much less False Positive Rate compared to many existing state of the art methods. The corresponding R code for the experiments is available at Github repository.

Error-Correcting Output Codes (ECOCs) offer a principled approach for combining simple binary classifiers into multiclass classifiers. In this paper, we investigate the problem of designing optimal ECOCs to achieve both nominal and adversarial accuracy using Support Vector Machines (SVMs) and binary deep learning models. In contrast to previous literature, we present an Integer Programming (IP) formulation to design minimal codebooks with desirable error correcting properties. Our work leverages the advances in IP solvers to generate codebooks with optimality guarantees. To achieve tractability, we exploit the underlying graph-theoretic structure of the constraint set in our IP formulation. This enables us to use edge clique covers to substantially reduce the constraint set. Our codebooks achieve a high nominal accuracy relative to standard codebooks (e.g., one-vs-all, one-vs-one, and dense/sparse codes). We also estimate the adversarial accuracy of our ECOC-based classifiers in a white-box setting. Our IP-generated codebooks provide non-trivial robustness to adversarial perturbations even without any adversarial training.

For mental disorders, patients' underlying mental states are non-observed latent constructs which have to be inferred from observed multi-domain measurements such as diagnostic symptoms and patient functioning scores. Additionally, substantial heterogeneity in the disease diagnosis between patients needs to be addressed for optimizing individualized treatment policy in order to achieve precision medicine. To address these challenges, we propose an integrated learning framework that can simultaneously learn patients' underlying mental states and recommend optimal treatments for each individual. This learning framework is based on the measurement theory in psychiatry for modeling multiple disease diagnostic measures as arising from the underlying causes (true mental states). It allows incorporation of the multivariate pre- and post-treatment outcomes as well as biological measures while preserving the invariant structure for representing patients' latent mental states. A multi-layer neural network is used to allow complex treatment effect heterogeneity. Optimal treatment policy can be inferred for future patients by comparing their potential mental states under different treatments given the observed multi-domain pre-treatment measurements. Experiments on simulated data and a real-world clinical trial data show that the learned treatment polices compare favorably to alternative methods on heterogeneous treatment effects, and have broad utilities which lead to better patient outcomes on multiple domains.

One of the most fundamental aspects of any machine learning algorithm is the training data used by the algorithm. We introduce the novel concept of ɛ- approximation of datasets, obtaining datasets which are much smaller than or are significant corruptions of the original training data while maintaining similar model performance. We introduce a meta-learning algorithm called Kernel Inducing Points (KIP) for obtaining such remarkable datasets, inspired by the recent developments in the correspondence between infinitely-wide neural networks and kernel ridge-regression (KRR). For KRR tasks, we demonstrate that KIP can compress datasets by one or two orders of magnitude, significantly improving previous dataset distillation and subset selection methods while obtaining state of the art results for MNIST and CIFAR-10 classification. Furthermore, our KIP -learned datasets are transferable to the training of finite-width neural networks even beyond the lazy-training regime, which leads to state of the art results for neural network dataset distillation with potential applications to privacy-preservation. Datasets are a pivotal component in any machine learning task. Typically, a machine learning problem regards a dataset as given and uses it to train a model according to some specific objective. In this work, we depart from the traditional paradigm by instead optimizing a dataset with respect to a learning objective, from which the resulting dataset can be used in a range of downstream learning tasks. Our work is directly motivated by several challenges in existing learning methods. Kernel methods or instance-based learning (Vinyals et al., 2016; Snell et al., 2017; Kaya & Bilge, 2019) in general require a support dataset to be deployed at inference time. Achieving good prediction accuracy typically requires having a large support set, which inevitably increases both memory footprint and latency at inference time--the scalability issue. It can also raise privacy concerns when deploying a support set of original examples, e.g., distributing raw images to user devices. Additional challenges to scalability include, for instance, the desire for rapid hyper-parameter search (Shleifer & Prokop, 2019) and minimizing the resources consumed when replaying data for continual learning (Borsos et al., 2020). A valuable contribution to all these problems would be to find surrogate datasets that can mitigate the challenges which occur for naturally occurring datasets without a significant sacrifice in performance.

We propose a tree-based algorithm for classification and regression problems in the context of functional data analysis, which allows to leverage representation learning and multiple splitting rules at the node level, reducing generalization error while retaining the interpretability of a tree. This is achieved by learning a weighted functional $L^{2}$ space by means of constrained convex optimization, which is then used to extract multiple weighted integral features from the input functions, in order to determine the binary split for each internal node of the tree. The approach is designed to manage multiple functional inputs and/or outputs, by defining suitable splitting rules and loss functions that can depend on the specific problem and can also be combined with scalar and categorical data, as the tree is grown with the original greedy CART algorithm. We focus on the case of scalar-valued functional inputs defined on unidimensional domains and illustrate the effectiveness of our method in both classification and regression tasks, through a simulation study and four real world applications.

Uplift is a particular case of individual treatment effect modeling. Such models deal with cause-and-effect inference for a specific factor, such as a marketing intervention. In practice, these models are built on customer data who purchased products or services to improve product marketing. Uplift is estimated using either i) conditional mean regression or ii) transformed outcome regression. Most existing approaches are adaptations of classification and regression trees for the uplift case. However, in practice, these conventional approaches are prone to overfitting. Here we propose a new method using neural networks. This representation allows to jointly optimize the difference in conditional means and the transformed outcome losses. As a consequence, the model not only estimates the uplift, but also ensures consistency in predicting the outcome. We focus on fully randomized experiments, which is the case of our data. We show our proposed method improves the state-of-the-art on synthetic and real data.

Machine learning with missing data has been approached in two different ways, including feature imputation where missing feature values are estimated based on observed values, and label prediction where downstream labels are learned directly from incomplete data. However, existing imputation models tend to have strong prior assumptions and cannot learn from downstream tasks, while models targeting label prediction often involve heuristics and can encounter scalability issues. Here we propose GRAPE, a graph-based framework for feature imputation as well as label prediction. GRAPE tackles the missing data problem using a graph representation, where the observations and features are viewed as two types of nodes in a bipartite graph, and the observed feature values as edges. Under the GRAPE framework, the feature imputation is formulated as an edge-level prediction task and the label prediction as a node-level prediction task. These tasks are then solved with Graph Neural Networks. Experimental results on nine benchmark datasets show that GRAPE yields 20% lower mean absolute error for imputation tasks and 10% lower for label prediction tasks, compared with existing state-of-the-art methods.