We describe a new library named picasso, which implements a unified framework of pathwise coordinate optimization for a variety of sparse learning problems (e.g., sparse linear regression, sparse logistic regression, sparse Poisson regression and scaled sparse linear regression) combined with efficient active set selection strategies. Besides, the library allows users to choose different sparsity-inducing regularizers, including the convex $\ell_1$, nonconvex MCP and SCAD regularizers. The library is coded in C++ and has user-friendly R and Python wrappers. Numerical experiments demonstrate that picasso can scale up to large problems efficiently.

Motivated by a wide variety of applications, ranging from stochastic optimization to dimension reduction through variable selection, the problem of estimating gradients accurately is of crucial importance in statistics and learning theory. We consider here the classic regression setup, where a real valued square integrable r.v. Y is to be predicted upon observing a (possibly high dimensional) random vector X by means of a predictive function f(X) as accurately as possible in the mean-squared sense and study a nearest-neighbour-based pointwise estimate of the gradient of the optimal predictive function, the regression function m(x) E[Y X x]. Under classic smoothness conditions combined with the assumption that the tails of Y m(X) are sub-Gaussian, we prove nonasymptotic bounds improving upon those obtained for alternative estimation methods. Beyond the novel theoretical results established, several illustrative numerical experiments have been carried out. The latter provide strong empirical evidence that the estimation method proposed works very well for various statistical problems involving gradient estimation, namely dimensionality reduction, stochastic gradient descent optimization and quantifying disentanglement.

Online Courses Udemy Deep Learning Prerequisites: Logistic Regression in Python, Data science techniques for professionals and students - learn the theory behind logistic regression and code in Python Created by Lazy Programmer Inc. English [Auto-generated], Portuguese [Auto-generated], 1 more Students also bought Natural Language Processing with Deep Learning in Python Data Science: Natural Language Processing (NLP) in Python Deep Learning: Advanced Computer Vision (GANs, SSD, More!) Unsupervised Machine Learning Hidden Markov Models in Python Modern Deep Learning in Python Preview this course GET COUPON CODE Description This course is a lead-in to deep learning and neural networks - it covers a popular and fundamental technique used in machine learning, data science and statistics: logistic regression. We cover the theory from the ground up: derivation of the solution, and applications to real-world problems. We show you how one might code their own logistic regression module in Python. This course does not require any external materials. Everything needed (Python, and some Python libraries) can be obtained for free.

Linear regression, also known as simple linear regression or bivariate linear regression, is used when we want to predict the value of a dependent variable based on the value of an independent variable. Included in this course is an e-book and a set of slides. The course is divided into two parts. In the first part, students are introduced to the theory behind linear regression. The theory is explained in an intuitive way.

Welcome to another blog on Logistic regression in python. In previous blog Logistic Regression for Machine Learning using Python, we saw univariate logistics regression. And we saw basic concepts on Binary classification, Sigmoid Curve, Likelihood function, and Odds and log odds. In, this section first will take a look at Multivariate Logistic regression concepts. And then we will be building a logistic regression in python.

Empirical risk minimization is perhaps the most influential idea in statistical learning, with applications to nearly all scientific and technical domains in the form of regression and classification models. To analyze massive streaming datasets in distributed computing environments, practitioners increasingly prefer to deploy regression models on edge rather than in the cloud. By keeping data on edge devices, we minimize the energy, communication, and data security risk associated with the model. Although it is equally advantageous to train models at the edge, a common assumption is that the model was originally trained in the cloud, since training typically requires substantial computation and memory. To this end, we propose STORM, an online sketch for empirical risk minimization. STORM compresses a data stream into a tiny array of integer counters. This sketch is sufficient to estimate a variety of surrogate losses over the original dataset. We provide rigorous theoretical analysis and show that STORM can estimate a carefully chosen surrogate loss for the least-squares objective. In an exhaustive experimental comparison for linear regression models on real-world datasets, we find that STORM allows accurate regression models to be trained.

Online machine learning systems need to adapt to domain shifts. Meanwhile, acquiring label at every timestep is expensive. We propose a surprisingly simple algorithm that adaptively balances its regret and its number of label queries in settings where the data streams are from a mixture of hidden domains. For online linear regression with oblivious adversaries, we provide a tight tradeoff that depends on the durations and dimensionalities of the hidden domains. Our algorithm can adaptively deal with interleaving spans of inputs from different domains. We also generalize our results to non-linear regression for hypothesis classes with bounded eluder dimension and adaptive adversaries. Experiments on synthetic and realistic datasets demonstrate that our algorithm achieves lower regret than uniform queries and greedy queries with equal labeling budget.

We study preconditioned gradient-based optimization methods where the preconditioning matrix has block-diagonal form. Such a structural constraint comes with the advantage that the update computation is block-separable and can be parallelized across multiple independent tasks. Our main contribution is to demonstrate that the convergence of these methods can significantly be improved by a randomization technique which corresponds to repartitioning coordinates across tasks during the optimization procedure. We provide a theoretical analysis that accurately characterizes the expected convergence gains of repartitioning and validate our findings empirically on various traditional machine learning tasks. From an implementation perspective, block-separable models are well suited for parallelization and, when shared memory is available, randomization can be implemented on top of existing methods very efficiently to improve convergence.

We consider machine learning, particularly regression, using locally-differentially private datasets. The Wasserstein distance is used to define an ambiguity set centered at the empirical distribution of the dataset corrupted by local differential privacy noise. The ambiguity set is shown to contain the probability distribution of unperturbed, clean data. The radius of the ambiguity set is a function of the privacy budget, spread of the data, and the size of the problem. Hence, machine learning with locally-differentially private datasets can be rewritten as a distributionally-robust optimization. For general distributions, the distributionally-robust optimization problem can relaxed as a regularized machine learning problem with the Lipschitz constant of the machine learning model as a regularizer. For linear and logistic regression, this regularizer is the dual norm of the model parameters. For Gaussian data, the distributionally-robust optimization problem can be solved exactly to find an optimal regularizer. This approach results in an entirely new regularizer for training linear regression models. Training with this novel regularizer can be posed as a semi-definite program. Finally, the performance of the proposed distributionally-robust machine learning training is demonstrated on practical datasets.

Behavior prediction plays an essential role in both autonomous driving systems and Advanced Driver Assistance Systems (ADAS), since it enhances vehicle's awareness of the imminent hazards in the surrounding environment. Many existing lane change prediction models take as input lateral or angle information and make short-term (< 5 seconds) maneuver predictions. In this study, we propose a longer-term (5~10 seconds) prediction model without any lateral or angle information. Three prediction models are introduced, including a logistic regression model, a multilayer perceptron (MLP) model, and a recurrent neural network (RNN) model, and their performances are compared by using the real-world NGSIM dataset. To properly label the trajectory data, this study proposes a new time-window labeling scheme by adding a time gap between positive and negative samples. Two approaches are also proposed to address the unstable prediction issue, where the aggressive approach propagates each positive prediction for certain seconds, while the conservative approach adopts a roll-window average to smooth the prediction. Evaluation results show that the developed prediction model is able to capture 75% of real lane change maneuvers with an average advanced prediction time of 8.05 seconds.