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.
Advanced Data Mining Projects with R takes you one step ahead in understanding the most complex data mining algorithms and implementing them in the popular R language. Follow up to our course Data Mining Projects in R, this course will teach you how to build your own recommendation engine. You will also implement dimensionality reduction and use it to build a real-world project. Going ahead, you will be introduced to the concept of neural networks and learn how to apply them for predictions, classifications, and forecasting. Finally, you will implement ggplot2, plotly and aspects of geomapping to create your own data visualization projects.By the end of this course, you will be well-versed with all the advanced data mining techniques and how to implement them using R, in any real-world scenario.
Then we invite you to check out this very friendly introduction we made at Udacity! There are actually 19 videos included in this playlist, covering topics like Linear Regression, Neural Networks, Hierarchical Clustering, and more. Really got the Machine Learning fever? Then consider enrolling in our Machine Learning Nanodegree program. It's the best way to learn everything you need to know to become a successful Machine Learning Engineer!
We consider the problem of reconstructing the dynamic state matrix of transmission power grids from time-stamped PMU measurements in the regime of ambient fluctuations. Using a maximum likelihood based approach, we construct a family of convex estimators that adapt to the structure of the problem depending on the available prior information. The proposed method is fully data-driven and does not assume any knowledge of system parameters. It can be implemented in near real-time and requires a small amount of data. Our learning algorithms can be used for model validation and calibration, and can also be applied to related problems of system stability, detection of forced oscillations, generation re-dispatch, as well as to the estimation of the system state.
In this paper, we study the online learning algorithm without explicit regularization terms. This algorithm is essentially a stochastic gradient descent scheme in a reproducing kernel Hilbert space (RKHS). The polynomially decaying step size in each iteration can play a role of regularization to ensure the generalization ability of online learning algorithm. We develop a novel capacity dependent analysis on the performance of the last iterate of online learning algorithm. The contribution of this paper is two-fold. First, our nice analysis can lead to the convergence rate in the standard mean square distance which is the best so far. Second, we establish, for the first time, the strong convergence of the last iterate with polynomially decaying step sizes in the RKHS norm. We demonstrate that the theoretical analysis established in this paper fully exploits the fine structure of the underlying RKHS, and thus can lead to sharp error estimates of online learning algorithm.
About this course: Using publicly available data from NASA of actual satellite observations of astronomical x-ray sources, we explore some of the mysteries of the cosmos, including neutron stars, black holes, quasars and supernovae. We will analyze energy spectra and time series data to understand how these incredible objects work. We utilize an imaging tool called DS9 to explore the amazing diversity of astronomical observations that have made x-ray astronomy one of the most active and exciting fields of scientific investigation in the past 50 years. Each week we will explore a different facet of x-ray astronomy. Beginning with an introduction to the nature of image formation, we then move on to examples of how our imaging program, DS9, can aid our understanding of real satellite data.
This course will explain how to use scikit-learn to do advanced machine learning. If you follow this course, you should be able to handle quite well a machine learning interview. Even though in that case you will need to study the math with more detail. We'll start by explaining what is the machine learning problem, methodology and terminology. We'll explain what are the differences between AI, machine learning (ML), statistics, and data mining.
We consider a variant of online convex optimization in which both the instances (input vectors) and the comparator (weight vector) are unconstrained. We exploit a natural scale invariance symmetry in our unconstrained setting: the predictions of the optimal comparator are invariant under any linear transformation of the instances. Our goal is to design online algorithms which also enjoy this property, i.e. are scale-invariant. We start with the case of coordinate-wise invariance, in which the individual coordinates (features) can be arbitrarily rescaled. We give an algorithm, which achieves essentially optimal regret bound in this setup, expressed by means of a coordinate-wise scale-invariant norm of the comparator. We then study general invariance with respect to arbitrary linear transformations. We first give a negative result, showing that no algorithm can achieve a meaningful bound in terms of scale-invariant norm of the comparator in the worst case. Next, we compliment this result with a positive one, providing an algorithm which "almost" achieves the desired bound, incurring only a logarithmic overhead in terms of the norm of the instances.
OpenCV is a library of programming functions mainly aimed at real-time computer vision. This course will show you how machine learning is great choice to solve real-word computer vision problems and how you can use the OpenCV modules to implement the popular machine learning concepts. The video will teach you how to work with the various OpenCV modules for statistical modelling and machine learning. You will start by preparing your data for analysis, learn about supervised and unsupervised learning, and see how to implement them with the help of real-world examples. The course will also show you how you can implement efficient models using the popular machine learning techniques such as classification, regression, decision trees, K-nearest neighbors, boosting, and neural networks with the aid of C and OpenCV.