A standard introduction to online learning might place Online Gradient Descent at its center and then proceed to develop generalizations and extensions like Online Mirror Descent and second-order methods. Here we explore the alternative approach of putting exponential weights (EW) first. We show that many standard methods and their regret bounds then follow as a special case by plugging in suitable surrogate losses and playing the EW posterior mean. For instance, we easily recover Online Gradient Descent by using EW with a Gaussian prior on linearized losses, and, more generally, all instances of Online Mirror Descent based on regular Bregman divergences also correspond to EW with a prior that depends on the mirror map. Furthermore, appropriate quadratic surrogate losses naturally give rise to Online Gradient Descent for strongly convex losses and to Online Newton Step. We further interpret several recent adaptive methods (iProd, Squint, and a variation of Coin Betting for experts) as a series of closely related reductions to exp-concave surrogate losses that are then handled by Exponential Weights. Finally, a benefit of our EW interpretation is that it opens up the possibility of sampling from the EW posterior distribution instead of playing the mean. As already observed by Bubeck and Eldan, this recovers the best-known rate in Online Bandit Linear Optimization.
This course not only covers machine learning techniques, it also covers in depth the rationale of investing strategy development. This course is the first of the Machine Learning for Finance and Algorithmic Trading & Investing Series. If you are looking for a course on applying machine learning to investing, the Machine Learning for Finance and Algorithmic Trading & Investing Series is for you. With over 30 machine learning techniques test cases, which included popular techniques such as Lasso regression, Ridge regression, SVM, XGBoost, random forest, Hidden Markov Model, common clustering techniques and many more, to get you started with applying Machine Learning to investing quickly.
Data science or data-driven science is one of today's fastest-growing fields. Are you looking for top Online courses on Data Science? Do you want to become a Data Scientist in 2017? Are you planning to buy a course for someone else to whom you do care? If your answer is yes, then you are in the right place.
One of the most challenging problems in kernel online learning is to bound the model size and to promote the model sparsity. Sparse models not only improve computation and memory usage, but also enhance the generalization capacity, a principle that concurs with the law of parsimony. However, inappropriate sparsity modeling may also significantly degrade the performance. In this paper, we propose Approximation Vector Machine (AVM), a model that can simultaneously encourage the sparsity and safeguard its risk in compromising the performance. When an incoming instance arrives, we approximate this instance by one of its neighbors whose distance to it is less than a predefined threshold. Our key intuition is that since the newly seen instance is expressed by its nearby neighbor the optimal performance can be analytically formulated and maintained. We develop theoretical foundations to support this intuition and further establish an analysis to characterize the gap between the approximation and optimal solutions. This gap crucially depends on the frequency of approximation and the predefined threshold. We perform the convergence analysis for a wide spectrum of loss functions including Hinge, smooth Hinge, and Logistic for classification task, and $l_1$, $l_2$, and $\epsilon$-insensitive for regression task. We conducted extensive experiments for classification task in batch and online modes, and regression task in online mode over several benchmark datasets. The results show that our proposed AVM achieved a comparable predictive performance with current state-of-the-art methods while simultaneously achieving significant computational speed-up due to the ability of the proposed AVM in maintaining the model size.
In recent years, we've seen a resurgence in AI, or artificial intelligence, and machine learning. Machine learning has led to some amazing results, like being able to analyze medical images and predict diseases on-par with human experts. Google's AlphaGo program was able to beat a world champion in the strategy game go using deep reinforcement learning. Machine learning is even being used to program self driving cars, which is going to change the automotive industry forever. Imagine a world with drastically reduced car accidents, simply by removing the element of human error.
About this course: Case Study - Predicting Housing Prices In our first case study, predicting house prices, you will create models that predict a continuous value (price) from input features (square footage, number of bedrooms and bathrooms,...). This is just one of the many places where regression can be applied. Other applications range from predicting health outcomes in medicine, stock prices in finance, and power usage in high-performance computing, to analyzing which regulators are important for gene expression. In this course, you will explore regularized linear regression models for the task of prediction and feature selection. You will be able to handle very large sets of features and select between models of various complexity.
A few weeks ago, I wrote about how and why I was learning Machine Learning, mainly through Andrew Ng's Coursera course. Machine Learning is built on prerequisites, so much so that learning by first principles seems overwhelming. Do you really need to spend a month learning linear algebra? You'll be okay if you have some math and programming experience. You really just have to be familiar with Sigma notation and be able to express it in a for loop. Sure, your assignments will take longer to complete and the first few times you see those giant equations your head will spin, but you can do this! Calculus is not even required.
The E-learning course starts by refreshing the basic concepts of the analytics process model: data preprocessing, analytics and post processing. We then discuss decision trees and ensemble methods (bagging, boosting, random forests), neural networks, support vector machines (SVMs), Bayesian networks, survival analysis, social networks, monitoring and backtesting analytical models. Throughout the course, we extensively refer to our industry and research experience. The E-learning course consists of more than 20 hours of movies, each 5 minutes on average. Quizzes are included to facilitate the understanding of the material.
Stochastic gradient descent (SGD) is commonly used for optimization in large-scale machine learning problems. Langford et al. (2009) introduce a sparse online learning method to induce sparsity via truncated gradient. With high-dimensional sparse data, however, the method suffers from slow convergence and high variance due to the heterogeneity in feature sparsity. To mitigate this issue, we introduce a stabilized truncated stochastic gradient descent algorithm. We employ a soft-thresholding scheme on the weight vector where the imposed shrinkage is adaptive to the amount of information available in each feature. The variability in the resulted sparse weight vector is further controlled by stability selection integrated with the informative truncation. To facilitate better convergence, we adopt an annealing strategy on the truncation rate, which leads to a balanced trade-off between exploration and exploitation in learning a sparse weight vector. Numerical experiments show that our algorithm compares favorably with the original algorithm in terms of prediction accuracy, achieved sparsity and stability.