Polynomial Regression is one of the important parts of Machine Learning. Polynomial Regression is a regression algorithm that frames a relationship between the independent variable(x) and dependent variable(y) as nth degree polynomial. Basically, it brings forth the finest estimation for dependent and independent variables. To convert the multiple linear regression into polynomial regression we need to add some polynomial terms. It acts as a saver when we have to deal with a dataset that is not linearly separable.

Causal inference is a hot topic in machine learning, and there are many excellent primers on the theory of causal inference available [1–4]. But much fewer examples of real-world applications of machine-learning-powered causal inference exist. This article introduces one such example from an industry context, using a (public) real-world dataset. It is aimed at a technical audience with an understanding of the basics of causality. Specifically, I will look at the "ideal" scenario of price elasticity estimation [2, 5].

We introduce Reflective Hamiltonian Monte Carlo (ReHMC), an HMC-based algorithm, to sample from a log-concave distribution restricted to a convex body. We prove that, starting from a warm start, the walk mixes to a log-concave target distribution $\pi(x) \propto e^{-f(x)}$, where $f$ is $L$-smooth and $m$-strongly-convex, within accuracy $\varepsilon$ after $\widetilde O(\kappa d^2 \ell^2 \log (1 / \varepsilon))$ steps for a well-rounded convex body where $\kappa = L / m$ is the condition number of the negative log-density, $d$ is the dimension, $\ell$ is an upper bound on the number of reflections, and $\varepsilon$ is the accuracy parameter. We also developed an efficient open source implementation of ReHMC and we performed an experimental study on various high-dimensional data-sets. The experiments suggest that ReHMC outperfroms Hit-and-Run and Coordinate-Hit-and-Run regarding the time it needs to produce an independent sample and introduces practical truncated sampling in thousands of dimensions.

Offensive Language detection in social media platforms has been an active field of research over the past years. In non-native English spoken countries, social media users mostly use a code-mixed form of text in their posts/comments. This poses several challenges in the offensive content identification tasks, and considering the low resources available for Tamil, the task becomes much harder. The current study presents extensive experiments using multiple deep learning, and transfer learning models to detect offensive content on YouTube. We propose a novel and flexible approach of selective translation and transliteration techniques to reap better results from fine-tuning and ensembling multilingual transformer networks like BERT, Distil- BERT, and XLM-RoBERTa. The experimental results showed that ULMFiT is the best model for this task. The best performing models were ULMFiT and mBERTBiLSTM for this Tamil code-mix dataset instead of more popular transfer learning models such as Distil- BERT and XLM-RoBERTa and hybrid deep learning models. The proposed model ULMFiT and mBERTBiLSTM yielded good results and are promising for effective offensive speech identification in low-resourced languages.

Deep Neural Networks are actively being used in the design of autonomous Cyber-Physical Systems (CPSs). The advantage of these models is their ability to handle high-dimensional state-space and learn compact surrogate representations of the operational state spaces. However, the problem is that the sampled observations used for training the model may never cover the entire state space of the physical environment, and as a result, the system will likely operate in conditions that do not belong to the training distribution. These conditions that do not belong to training distribution are referred to as Out-of-Distribution (OOD). Detecting OOD conditions at runtime is critical for the safety of CPS. In addition, it is also desirable to identify the context or the feature(s) that are the source of OOD to select an appropriate control action to mitigate the consequences that may arise because of the OOD condition. In this paper, we study this problem as a multi-labeled time series OOD detection problem over images, where the OOD is defined both sequentially across short time windows (change points) as well as across the training data distribution. A common approach to solving this problem is the use of multi-chained one-class classifiers. However, this approach is expensive for CPSs that have limited computational resources and require short inference times. Our contribution is an approach to design and train a single $\beta$-Variational Autoencoder detector with a partially disentangled latent space sensitive to variations in image features. We use the feature sensitive latent variables in the latent space to detect OOD images and identify the most likely feature(s) responsible for the OOD. We demonstrate our approach using an Autonomous Vehicle in the CARLA simulator and a real-world automotive dataset called nuImages.

To date, several automated strategies for identification/segmentation of Multiple Sclerosis (MS) lesions by Magnetic Resonance Imaging (MRI) have been presented which are either outperformed by human experts or, at least, whose results are well distinguishable from humans. This is due to the ambiguity originated by MRI instabilities, peculiar MS Heterogeneity and MRI unspecific nature with respect to MS. Physicians partially treat the uncertainty generated by ambiguity relying on personal radiological/clinical/anatomical background and experience. We present an automated framework for MS lesions identification/segmentation based on three pivotal concepts to better emulate human reasoning: the modeling of uncertainty; the proposal of two, separately trained, CNN, one optimized with respect to lesions themselves and the other to the environment surrounding lesions, respectively repeated for axial, coronal and sagittal directions; the ensemble of the CNN output. The proposed framework is trained, validated and tested on the 2016 MSSEG benchmark public data set from a single imaging modality, FLuid-Attenuated Inversion Recovery (FLAIR). The comparison, performed on the segmented lesions by means of most of the metrics normally used with respect to the ground-truth and the 7 human raters in MSSEG, prove that there is no significant difference between the proposed framework and the other raters. Results are also shown for the uncertainty, though a comparison with the other raters is impossible.

Network-based algorithms are used in most domains of research and industry in a wide variety of applications and are of great practical use. In this work, we demonstrate subnetwork detection based on multi-modal node features using a new Greedy Decision Forest for better interpretability. The latter will be a crucial factor in retaining experts and gaining their trust in such algorithms in the future. To demonstrate a concrete application example, we focus in this paper on bioinformatics and systems biology with a special focus on biomedicine. However, our methodological approach is applicable in many other domains as well. Systems biology serves as a very good example of a field in which statistical data-driven machine learning enables the analysis of large amounts of multi-modal biomedical data. This is important to reach the future goal of precision medicine, where the complexity of patients is modeled on a system level to best tailor medical decisions, health practices and therapies to the individual patient. Our glass-box approach could help to uncover disease-causing network modules from multi-omics data to better understand diseases such as cancer.

Modern methods for learning from data depend on many tuning parameters, such as the stepsize for optimization methods, and the regularization strength for regularized learning methods. Since performance can depend strongly on these parameters, it is important to develop comparisons between \emph{classes of methods}, not just for particularly tuned ones. Here, we take aim to compare classes of estimators via the relative performance of the \emph{best method in the class}. This allows us to rigorously quantify the tuning sensitivity of learning algorithms. As an illustration, we investigate the statistical estimation performance of ridge regression with a uniform grid of regularization parameters, and of gradient descent iterates with a fixed stepsize, in the standard linear model with a random isotropic ground truth parameter. (1) For orthogonal designs, we find the \emph{exact minimax optimal classes of estimators}, showing they are equal to gradient descent with a polynomially decaying learning rate. We find the exact suboptimalities of ridge regression and gradient descent with a fixed stepsize, showing that they decay as either $1/k$ or $1/k^2$ for specific ranges of $k$ estimators. (2) For general designs with a large number of non-zero eigenvalues, we find that gradient descent outperforms ridge regression when the eigenvalues decay slowly, as a power law with exponent less than unity. If instead the eigenvalues decay quickly, as a power law with exponent greater than unity or exponentially, we find that ridge regression outperforms gradient descent. Our results highlight the importance of tuning parameters. In particular, while optimally tuned ridge regression is the best estimator in our case, it can be outperformed by gradient descent when both are restricted to being tuned over a finite regularization grid.

Rest is essential for a high-level physiological and psychological performance. It is also necessary for the muscles to repair, rebuild, and strengthen. There is a significant correlation between the quality of rest and the resting posture. Therefore, identification of the resting position is of paramount importance to maintain a healthy life. Resting postures can be classified into four basic categories: Lying on the back (supine), facing of the left / right sides and free-fall position. The later position is already considered to be an unhealthy posture by researchers equivocally and hence can be eliminated. In this paper, we analyzed the other three states of resting position based on the data collected from the physiological parameters: Electrogastrogram (EGG), Electrocardiogram (ECG), Respiration Rate, Heart Rate, and Oxygen Saturation (SpO2). Based on these parameters, the resting position is classified using a hybrid stacked ensemble machine learning model designed using the Decision tree, Random Forest, and Xgboost algorithms. Our study demonstrates a 100% accurate prediction of the resting position using the hybrid model. The proposed method of identifying the resting position based on physiological parameters has the potential to be integrated into wearable devices. This is a low cost, highly accurate and autonomous technique to monitor the body posture while maintaining the user privacy by eliminating the use of RGB camera conventionally used to conduct the polysomnography (sleep Monitoring) or resting position studies.

Item Response Theory (IRT) is a ubiquitous model for understanding human behaviors and attitudes based on their responses to questions. Large modern datasets offer opportunities to capture more nuances in human behavior, potentially improving psychometric modeling leading to improved scientific understanding and public policy. However, while larger datasets allow for more flexible approaches, many contemporary algorithms for fitting IRT models may also have massive computational demands that forbid real-world application. To address this bottleneck, we introduce a variational Bayesian inference algorithm for IRT, and show that it is fast and scalable without sacrificing accuracy. Applying this method to five large-scale item response datasets from cognitive science and education yields higher log likelihoods and higher accuracy in imputing missing data than alternative inference algorithms. Using this new inference approach we then generalize IRT with expressive Bayesian models of responses, leveraging recent advances in deep learning to capture nonlinear item characteristic curves (ICC) with neural networks. Using an eigth-grade mathematics test from TIMSS, we show our nonlinear IRT models can capture interesting asymmetric ICCs. The algorithm implementation is open-source, and easily usable.