In order to explain the differences between alternative approaches to estimating the parameters of a model, let's take a look at a concrete example: Ordinary Least Squares (OLS) Linear Regression. In Ordinary Least Squares (OLS) Linear Regression, our goal is to find the line (or hyperplane) that minimizes the vertical offsets. Or, in other words, we define the best-fitting line as the line that minimizes the sum of squared errors (SSE) or mean squared error (MSE) between our target variable (y) and our predicted output over all samples i in our dataset of size n. The closed-form solution may (should) be preferred for "smaller" datasets -- if computing (a "costly") matrix inverse is not a concern. For very large datasets, or datasets where the inverse of XTX may not exist (the matrix is non-invertible or singular, e.g., in case of perfect multicollinearity), the GD or SGD approaches are to be preferred.

Lots of analyst misinterpret the term'boosting' used in data science. Let me provide an interesting explanation of this term. Boosting grants power to machine learning models to improve their accuracy of prediction. Boosting algorithms are one of the most widely used algorithm in data science competitions. The winners of our last hackathons agree that they try boosting algorithm to improve accuracy of their models.

In my last post, I have explained about MSE, today I will explain the variance & bias trade-off, Precision recall trade-off while assessing the model accuracy. Variance refers to the amount by which the estimated output (f) would change if we estimated it (f) using a different training dataset. Since the training data is used to fit the statistical learning method, different training sets will result in different outputs (f). Ideally, the estimate should not vary much between training sets. Bias refers to the error that is introduced by approximating a complicated problem by a simpler model.

What is Vector based word classification? Are you sure you don't mean support vector machine based word classification (like you did last time)? If not, then your boss probably means word2vec-style learning. That isn't really a classification method on its own, although it is possible to build classifiers on top of it. It's about a tool that mines texts from documents and then creates some kind of analysis based on that.

Creating mood sensing technology has become very popular in recent years. There is a wide range of companies trying to detect your emotions from what you write, the tone of your voice, or from the expressions on your face. All of these companies offer their technology online through cloud-based programming interfaces (APIs). As part of my offline emotion sensing hardware (Project Jammin), I have already built early prototypes of facial expression and speech content recognition for emotion detection. In this short article I describe the missing part, a voice tone analyzer.

If you are a software developer who wants to learn how machine learning models work and how to apply them effectively, this book is for you. Familiarity with machine learning fundamentals and Python will be helpful, but is not essential. This book examines machine learning models including logistic regression, decision trees, and support vector machines, and applies them to common problems such as categorizing documents and classifying images. It begins with the fundamentals of machine learning, introducing you to the supervised-unsupervised spectrum, the uses of training and test data, and evaluating models. You will learn how to use generalized linear models in regression problems, as well as solve problems with text and categorical features. You will be acquainted with the use of logistic regression, regularization, and the various loss functions that are used by generalized linear models.

Accelerated coordinate descent is widely used in optimization due to its cheap per-iteration cost and scalability to large-scale problems. Up to a primal-dual transformation, it is also the same as accelerated stochastic gradient descent that is one of the central methods used in machine learning. In this paper, we improve the best known running time of accelerated coordinate descent by a factor up to $\sqrt{n}$. Our improvement is based on a clean, novel non-uniform sampling that selects each coordinate with a probability proportional to the square root of its smoothness parameter. Our proof technique also deviates from the classical estimation sequence technique used in prior work. Our speed-up applies to important problems such as empirical risk minimization and solving linear systems, both in theory and in practice.

We explore a novel approach to semi-supervised learning. This approach is contrary to the common approach in that the unlabeled examples serve to "muffle," rather than enhance, the guidance provided by the labeled examples. We provide several variants of the basic algorithm and show experimentally that they can achieve significantly higher AUC than boosted trees, random forests and logistic regression when unlabeled examples are available.

We study the stochastic Riemannian gradient algorithm for matrix eigen-decomposition. The state-of-the-art stochastic Riemannian algorithm requires the learning rate to decay to zero and thus suffers from slow convergence and sub-optimal solutions. In this paper, we address this issue by deploying the variance reduction (VR) technique of stochastic gradient descent (SGD). The technique was originally developed to solve convex problems in the Euclidean space. We generalize it to Riemannian manifolds and realize it to solve the non-convex eigen-decomposition problem. We are the first to propose and analyze the generalization of SVRG to Riemannian manifolds. Specifically, we propose the general variance reduction form, SVRRG, in the framework of the stochastic Riemannian gradient optimization. It's then specialized to the problem with eigensolvers and induces the SVRRG-EIGS algorithm. We provide a novel and elegant theoretical analysis on this algorithm. The theory shows that a fixed learning rate can be used in the Riemannian setting with an exponential global convergence rate guaranteed. The theoretical results make a significant improvement over existing studies, with the effectiveness empirically verified.

Despite being the standard loss function to train multi-class neural networks, the log-softmax has two potential limitations. First, it involves computations that scale linearly with the number of output classes, which can restrict the size of problems we are able to tackle with current hardware. Second, it remains unclear how close it matches the task loss such as the top-k error rate or other non-differentiable evaluation metrics which we aim to optimize ultimately. In this paper, we introduce an alternative classification loss function, the Z-loss, which is designed to address these two issues. Unlike the log-softmax, it has the desirable property of belonging to the spherical loss family (Vincent et al., 2015), a class of loss functions for which training can be performed very efficiently with a complexity independent of the number of output classes. We show experimentally that it significantly outperforms the other spherical loss functions previously investigated. Furthermore, we show on a word language modeling task that it also outperforms the log-softmax with respect to certain ranking scores, such as top-k scores, suggesting that the Z-loss has the flexibility to better match the task loss. These qualities thus makes the Z-loss an appealing candidate to train very efficiently large output networks such as word-language models or other extreme classification problems. On the One Billion Word (Chelba et al., 2014) dataset, we are able to train a model with the Z-loss 40 times faster than the log-softmax and more than 4 times faster than the hierarchical softmax.