Hello and welcome to this tutorial. We have learnt how to create Single and Multiple linear regression models. Now, let’s learn how to create Polynomial regression Models in R and where we would apply it to solve real life problems. According to Wikipedia, Polynomial regression is a form of regression analysis in which the relationship between the independent variable x and the dependent variable y is modeled as an nth degree polynomial in x. Polynomial regression fits a nonlinear relationship between the value of x and the correspondent conditional mean of y. In this tutorial we are going to be […]

This is a continuously updated repository that documents personal journey on learning data science, machine learning related topics. The content aims to strike a good balance between mathematical notations, educational implementation from scratch using Python's scientific stack including numpy, numba, scipy, pandas, matplotlib, pyspark etc. and open-source library usage such as scikit-learn, fasttext, huggingface, onnx, xgboost, lightgbm, pytorch, keras, tensorflow, gensim, h2o, ortools, ray tune etc. Notes related to advertising domain. Information Retrieval, some examples are demonstrated using ElasticSearch. End to end project including data preprocessing, model building. Includes: Quick review of necessary statistic concepts.

Simulations of large-scale dynamical systems require expensive computations. Low-dimensional parametrization of high-dimensional states such as Proper Orthogonal Decomposition (POD) can be a solution to lessen the burdens by providing a certain compromise between accuracy and model complexity. However, for really low-dimensional parametrizations (for example for controller design) linear methods like the POD come to their natural limits so that nonlinear approaches will be the methods of choice. In this work we propose a convolutional autoencoder (CAE) consisting of a nonlinear encoder and an affine linear decoder and consider combinations with k-means clustering for improved encoding performance. The proposed set of methods is compared to the standard POD approach in two cylinder-wake scenarios modeled by the incompressible Navier-Stokes equations.

Missing data is common in applied data science, particularly for tabular data sets found in healthcare, social sciences, and natural sciences. Most supervised learning methods only work on complete data, thus requiring preprocessing such as missing value imputation to work on incomplete data sets. However, imputation alone does not encode useful information about the missing values themselves. For data sets with informative missing patterns, the Missing Indicator Method (MIM), which adds indicator variables to indicate the missing pattern, can be used in conjunction with imputation to improve model performance. While commonly used in data science, MIM is surprisingly understudied from an empirical and especially theoretical perspective. In this paper, we show empirically and theoretically that MIM improves performance for informative missing values, and we prove that MIM does not hurt linear models asymptotically for uninformative missing values. Additionally, we find that for high-dimensional data sets with many uninformative indicators, MIM can induce model overfitting and thus test performance. To address this issue, we introduce Selective MIM (SMIM), a novel MIM extension that adds missing indicators only for features that have informative missing patterns. We show empirically that SMIM performs at least as well as MIM in general, and improves MIM for high-dimensional data. Lastly, to demonstrate the utility of MIM on real-world data science tasks, we demonstrate the effectiveness of MIM and SMIM on clinical tasks generated from the MIMIC-III database of electronic health records.

We study the relationship between two desiderata of algorithms in statistical inference and machine learning: differential privacy and robustness to adversarial data corruptions. Their conceptual similarity was first observed by Dwork and Lei (STOC 2009), who observed that private algorithms satisfy robustness, and gave a general method for converting robust algorithms to private ones. However, all general methods for transforming robust algorithms into private ones lead to suboptimal error rates. Our work gives the first black-box transformation that converts any adversarially robust algorithm into one that satisfies pure differential privacy. Moreover, we show that for any low-dimensional estimation task, applying our transformation to an optimal robust estimator results in an optimal private estimator. Thus, we conclude that for any low-dimensional task, the optimal error rate for $\varepsilon$-differentially private estimators is essentially the same as the optimal error rate for estimators that are robust to adversarially corrupting $1/\varepsilon$ training samples. We apply our transformation to obtain new optimal private estimators for several high-dimensional tasks, including Gaussian (sparse) linear regression and PCA. Finally, we present an extension of our transformation that leads to approximate differentially private algorithms whose error does not depend on the range of the output space, which is impossible under pure differential privacy.

Slope failures possess destructive power that can cause significant damage to both life and infrastructure. Monitoring slopes prone to instabilities is therefore critical in mitigating the risk posed by their failure. The purpose of slope monitoring is to detect precursory signs of stability issues, such as changes in the rate of displacement with which a slope is deforming. This information can then be used to predict the timing or probability of an imminent failure in order to provide an early warning. In this study, a more objective, statistical-learning algorithm is proposed to detect and characterise the risk of a slope failure, based on spectral analysis of serially correlated displacement time series data. The algorithm is applied to satellite-based interferometric synthetic radar (InSAR) displacement time series data to retrospectively analyse the risk of the 2019 Brumadinho tailings dam collapse in Brazil. Two potential risk milestones are identified and signs of a definitive but emergent risk (27 February 2018 to 26 August 2018) and imminent risk of collapse of the tailings dam (27 June 2018 to 24 December 2018) are detected by the algorithm. Importantly, this precursory indication of risk of failure is detected as early as at least five months prior to the dam collapse on 25 January 2019. The results of this study demonstrate that the combination of spectral methods and second order statistical properties of InSAR displacement time series data can reveal signs of a transition into an unstable deformation regime, and that this algorithm can provide sufficient early warning that could help mitigate catastrophic slope failures.

AI constructivism as inspired by Jean Piaget, described and surveyed by Frank Guerin, and representatively implemented by Gary Drescher seeks to create algorithms and knowledge structures that enable agents to acquire, maintain, and apply a deep understanding of the environment through sensorimotor interactions. This paper aims to increase awareness of constructivist AI implementations to encourage greater progress toward enabling lifelong learning by machines. It builds on Guerin's 2008 "Learning Like a Baby: A Survey of AI approaches." After briefly recapitulating that survey, it summarizes subsequent progress by the Guerin referents, numerous works not covered by Guerin (or found in other surveys), and relevant efforts in related areas. The focus is on knowledge representations and learning algorithms that have been used in practice viewed through lenses of Piaget's schemas, adaptation processes, and staged development. The paper concludes with a preview of a simple framework for constructive AI being developed by the author that parses concepts from sensory input and stores them in a semantic memory network linked to episodic data.

These automated decision frameworks have demonstrated various unwanted consequences as a result of biased data [11, 66-68, 84, 86, 109]. Oftentimes these systems are trained on samples (datasets) from a larger population. Biased results can arise if the sample does not accurately represent the target population, or if there is a lack of sufficient representation for subgroups within the data. While the literature of data bias in machine Learning and artificial intelligence (AI) systems is rich [99], there exists only limited work on the connections between data representativity and AI systems. Terms like representative sample are used ubiquitously in the literature, often without further specification on the details or effects of this representativity. This paper analyzes and surveys data representativity in scientific literature relating to machine learning and AI systems by investigating how different notions of representativity are used and what effects adhering to different notions of data representativity has in relation to appropriate inference. The term representative sample is an overloaded term and a generally accepted definition of what constitutes a representative sample (subset of observations) is hard to find in the literature. A few examples demonstrate that at least a couple of definitions of representative sample exist. The most general definition we found is from D'Excelle (2014) and states ""Representative sampling" is a type of statistical sampling that allows us to use data from a sample to make conclusions that are representative for the population from which the sample is taken."

A plethora of recent research has proposed several automated methods based on machine learning (ML) and deep learning (DL) to detect cybersickness in Virtual reality (VR). However, these detection methods are perceived as computationally intensive and black-box methods. Thus, those techniques are neither trustworthy nor practical for deploying on standalone VR head-mounted displays (HMDs). This work presents an explainable artificial intelligence (XAI)-based framework VR-LENS for developing cybersickness detection ML models, explaining them, reducing their size, and deploying them in a Qualcomm Snapdragon 750G processor-based Samsung A52 device. Specifically, we first develop a novel super learning-based ensemble ML model for cybersickness detection. Next, we employ a post-hoc explanation method, such as SHapley Additive exPlanations (SHAP), Morris Sensitivity Analysis (MSA), Local Interpretable Model-Agnostic Explanations (LIME), and Partial Dependence Plot (PDP) to explain the expected results and identify the most dominant features. The super learner cybersickness model is then retrained using the identified dominant features. Our proposed method identified eye tracking, player position, and galvanic skin/heart rate response as the most dominant features for the integrated sensor, gameplay, and bio-physiological datasets. We also show that the proposed XAI-guided feature reduction significantly reduces the model training and inference time by 1.91X and 2.15X while maintaining baseline accuracy. For instance, using the integrated sensor dataset, our reduced super learner model outperforms the state-of-the-art works by classifying cybersickness into 4 classes (none, low, medium, and high) with an accuracy of 96% and regressing (FMS 1-10) with a Root Mean Square Error (RMSE) of 0.03.

Tabular data is a common form of organizing data. Multiple models are available to generate synthetic tabular datasets where observations are independent, but few have the ability to produce relational datasets. Modeling relational data is challenging as it requires modeling both a "parent" table and its relationships across tables. We introduce REaLTabFormer (Realistic Relational and Tabular Transformer), a tabular and relational synthetic data generation model. It first creates a parent table using an autoregressive GPT-2 model, then generates the relational dataset conditioned on the parent table using a sequence-to-sequence (Seq2Seq) model. We implement target masking to prevent data copying and propose the $Q_{\delta}$ statistic and statistical bootstrapping to detect overfitting. Experiments using real-world datasets show that REaLTabFormer captures the relational structure better than a baseline model. REaLTabFormer also achieves state-of-the-art results on prediction tasks, "out-of-the-box", for large non-relational datasets without needing fine-tuning.