A model can be considered as transparent when it (or all parts of it) can be fully understood as such, or when the learning process is understandable. A natural and common candidate that fits, at first sight, these criteria is the linear regression algorithm, where coefficients are usually seen as the individual contributions of the input features. Another candidate is the decision tree approach where model predictions can be broken down into a series of understandable operations. One can reasonably consider these models as transparent: one can easily identify the features that were used to take the decision. However, one may need to be cautious not to push too far the medical interpretation.

We propose the AdaPtive Noise Augmentation (PANDA) procedure to regularize the estimation and inference of generalized linear models (GLMs). PANDA iteratively optimizes the objective function given noise augmented data until convergence to obtain the regularized model estimates. The augmented noises are designed to achieve various regularization effects, including $l_0$, bridge (lasso and ridge included), elastic net, adaptive lasso, and SCAD, as well as group lasso and fused ridge. We examine the tail bound of the noise-augmented loss function and establish the almost sure convergence of the noise-augmented loss function and its minimizer to the expected penalized loss function and its minimizer, respectively. We derive the asymptotic distributions for the regularized parameters, based on which, inferences can be obtained simultaneously with variable selection. PANDA exhibits ensemble learning behaviors that help further decrease the generalization error. Computationally, PANDA is easy to code, leveraging existing software for implementing GLMs, without resorting to complicated optimization techniques. We demonstrate the superior or similar performance of PANDA against the existing approaches of the same type of regularizers in simulated and real-life data. We show that the inferences through PANDA achieve nominal or near-nominal coverage and are far more efficient compared to a popular existing post-selection procedure.

Feature Scaling: The dataset may contain more than 1 column and in that case, if the range of one of the columns is 100–1000 and the other column is 0–1. Then linear regression may give more weightage to the first column than the other column because of its high value. That is why it is good to always scale your data before fitting the model. Linear Assumption: This is kinda self-explanatory. As the algorithm is literally named Linear Regression, it will not be able to handle data that does not fit into linear behavior.

This course will be your guide to learning how to use the power of theory, math and python to create linear regression and logistic regression, two of most popular and useful machine learning models from scratch. This course is designed for folks with some programming experience or experienced developers looking to make the jump to data science and machine learning, I'll teach you how to dive deep into the math behind the linear models in an easy and understandable way. Once, you have understood the inner workings of the linear models and uncovered the black box, you are ready to code everything from the ground up without using any fancy ready made machine learning libraries and yes you will be taught that too! The course is beneficial for understanding the machine learning concepts deeply rather than just using some library to get results, it will guide you in the right direction for learning many other machine learning and deep learning algorithms, as this course covers all the basics required, you will be well on your way to becoming an expert Data Scientist! Since this course goes deep into the math and has coding from scratch, a basic to intermediate knowledge of coding is a must, also good idea of derivatives(calculus), linear algebra(matrix multiplication) and basic probability is required to get the full out of this course.

The course covers Machine Learning in exhaustive way. The presentations and hands-on practical are made such that it's made easy. The knowledge gained through this tutorial series can be applied to various real world scenarios. UnSupervised learning does not require to supervise the model. Instead, it allows the model to work on its own to discover patterns and information that was previously undetected. It mainly deals with the unlabeled data.

The accuracy of the estimated stellar atmospheric parameter decreases evidently with the decreasing of spectral signal-to-noise ratio (SNR) and there are a huge amount of this kind observations, especially in case of SNR$<$30. Therefore, it is helpful to improve the parameter estimation performance for these spectra and this work studied the ($T_\texttt{eff}, \log~g$, [Fe/H]) estimation problem for LAMOST DR8 low-resolution spectra with 20$\leq$SNR$<$30. We proposed a data-driven method based on machine learning techniques. Firstly, this scheme detected stellar atmospheric parameter-sensitive features from spectra by the Least Absolute Shrinkage and Selection Operator (LASSO), rejected ineffective data components and irrelevant data. Secondly, a Multi-layer Perceptron (MLP) method was used to estimate stellar atmospheric parameters from the LASSO features. Finally, the performance of the LASSO-MLP was evaluated by computing and analyzing the consistency between its estimation and the reference from the APOGEE (Apache Point Observatory Galactic Evolution Experiment) high-resolution spectra. Experiments show that the Mean Absolute Errors (MAE) of $T_\texttt{eff}, \log~g$, [Fe/H] are reduced from the LASP (137.6 K, 0.195 dex, 0.091 dex) to LASSO-MLP (84.32 K, 0.137 dex, 0.063 dex), which indicate evident improvements on stellar atmospheric parameter estimation. In addition, this work estimated the stellar atmospheric parameters for 1,162,760 low-resolution spectra with 20$\leq$SNR$<$30 from LAMOST DR8 using LASSO-MLP, and released the estimation catalog, learned model, experimental code, trained model, training data and test data for scientific exploration and algorithm study.

This paper presents a method for jointly estimating the state, input, and parameters of linear systems in an online fashion. The method is specially designed for measurements that are corrupted with non-Gaussian noise or outliers, which are commonly found in engineering applications. In particular, it combines recursive, alternating, and iteratively-reweighted least squares into a single, one-step algorithm, which solves the estimation problem online and benefits from the robustness of least-deviation regression methods. The convergence of the iterative method is formally guaranteed. Numerical experiments show the good performance of the estimation algorithm in presence of outliers and in comparison to state-of-the-art methods.

The R-square is a measure of how well the linear regression model fits the observed data. It is calculated by squaring the correlation coefficient and dividing by the standard deviation of errors. It is the square of the correlation coefficient divided by its standard deviation (r2/s2). The R-square value of 1 indicates that the model explains 100% of the variation in Y. The R-square values greater than 1 indicate that the model explains more than 100% of the variation in Y.

Evaluation metrics to analyze the performance of models. Different methods to deal with imbalanced data. Implementation of Content and Collaborative based filtering. Implementation of Different algorithms used for Time Series forecasting. Evaluation metrics to analyze the performance of models.

'The quantile function is a mathematical function that takes a quantile (a percentage of a distribution ranging from 0 to 1) as an input and returns the value of a variable as an output.' It can answer queries such as, "How much inventory do I need to maintain on hand if I want to guarantee that 95 percent of my customers receive their orders within 24 hours?" As a result, the quantile function is frequently utilized in forecasting questions. However, in practice, there is rarely a neat method for computing the quantile function. That means that if you want to compute it for a different quantile, you'll need to create a new regression model, which nowadays usually entails retraining a neural network.