The information bottleneck (IB) approach to clustering takes a joint distribution $P\!\left(X,Y\right)$ and maps the data $X$ to cluster labels $T$ which retain maximal information about $Y$ (Tishby et al., 1999). This objective results in an algorithm that clusters data points based upon the similarity of their conditional distributions $P\!\left(Y\mid X\right)$. This is in contrast to classic "geometric clustering" algorithms such as $k$-means and gaussian mixture models (GMMs) which take a set of observed data points $\left\{ \mathbf{x}_{i}\right\}_{i=1:N}$ and cluster them based upon their geometric (typically Euclidean) distance from one another. Here, we show how to use the deterministic information bottleneck (DIB) (Strouse and Schwab, 2017), a variant of IB, to perform geometric clustering, by choosing cluster labels that preserve information about data point location on a smoothed dataset. We also introduce a novel intuitive method to choose the number of clusters, via kinks in the information curve. We apply this approach to a variety of simple clustering problems, showing that DIB with our model selection procedure recovers the generative cluster labels. We also show that, for one simple case, DIB interpolates between the cluster boundaries of GMMs and $k$-means in the large data limit. Thus, our IB approach to clustering also provides an information-theoretic perspective on these classic algorithms.

A novel quantile Fourier neural network is presented for nonparametric probabilistic forecasting. Prediction are provided in the form of composite quantiles using time as the only input to the model. This effectively is a form of extrapolation based quantile regression applied for forecasting. Empirical results showcase that for time series data that have clear seasonality and trend, the model provides high quality probabilistic predictions. This work introduces a new class of forecasting of using only time as the input versus using past data such as an autoregressive model. Extrapolation based regression has not been studied before for probabilistic forecasting.

Tensor regression networks achieve high rate of compression of model parameters in multilayer perceptrons (MLP) while having slight impact on performances. Tensor regression layer imposes low-rank constraints on the tensor regression layer which replaces the flattening operation of traditional MLP. We investigate tensor regression networks using various low-rank tensor approximations, aiming to leverage the multi-modal structure of high dimensional data by enforcing efficient low-rank constraints. We provide a theoretical analysis giving insights on the choice of the rank parameters. We evaluated performance of proposed model with state-of-the-art deep convolutional models. For CIFAR-10 dataset, we achieved the compression rate of 0.018 with the sacrifice of accuracy less than 1%.

In high dimensional regression settings, sparsity enforcing penalties have proved useful to regularize the data-fitting term. A recently introduced technique called screening rules propose to ignore some variables in the optimization leveraging the expected sparsity of the solutions and consequently leading to faster solvers. When the procedure is guaranteed not to discard variables wrongly the rules are said to be safe. In this work, we propose a unifying framework for generalized linear models regularized with standard sparsity enforcing penalties such as $\ell_1$ or $\ell_1/\ell_2$ norms. Our technique allows to discard safely more variables than previously considered safe rules, particularly for low regularization parameters. Our proposed Gap Safe rules (so called because they rely on duality gap computation) can cope with any iterative solver but are particularly well suited to (block) coordinate descent methods. Applied to many standard learning tasks, Lasso, Sparse-Group Lasso, multi-task Lasso, binary and multinomial logistic regression, etc., we report significant speed-ups compared to previously proposed safe rules on all tested data sets.

This is an introductory course to Simple Linear Regression, one of the most basic courses in Statistics. This course is most suitable for students of professionals with basic knowledge or beginning level in Statistics and R coding. It also fits for anybody who want to explore the field of statistics using R in any discipline. We will start with an introduction section where I will explain the regression equation with a detailed example. Next, we will cover the essentials of modeling.

Smart City has been selected as our primary use case in IoT for three reasons: Firstly, among all of the reviewed articles the focus of 60 percents is on the field of the Smart City, secondly, Smart City includes many of the other use cases in IoT, and thirdly, there are many open datasets for Smart City applications easily accessible for researchers. Also, Support Vector Machine (SVM) algorithm is implemented on the Aarhus City smart traffic data in order to predict traffic hours during one day in Section 6. By answering the above questions about the IoT smart data and machine learning algorithms, we would be able to choose the best machine learning algorithm that can handle IoT smart data characteristics. Unlike the others, similar surveys about the machine learning and IoT, readers of this article would be able to get deep and technical understanding of machine learning algorithms, IoT applications, and IoT data characteristics along with both technical and simple implementations.

They are powerful data mining techniques that allow you to detect patterns in your data or variables. For each technique, a number of practical exercises are proposed. By doing these exercises you'll actually apply in practice what you have learned. This course is your opportunity to become a machine learning expert in a few weeks only! With my video lectures, you will find it very easy to master the major machine learning techniques. Everything is shown live, step by step, so you can replicate any procedure at any time you need it. So click the "Enroll" button to get instant access to your machine learning course. It will surely provide you with new priceless skills. And, who knows, it could give you a tremendous career boost in the near future.

Data parallelism is a popular technique used to speed up training on large mini-batches when each mini-batch is too large to fit on a GPU. Under data parallelism, a mini-batch is split up into smaller sized batches that are small enough to fit on the memory available on different GPUs on the network. Each GPU holds an identical copy of the network parameters and runs the forward and backward pass. At the end of the backward pass, each GPU sends the computed gradients to a parameter server. The parameter server aggregates the gradients and computes the updates to the network parameters using some variant of Stochastic Gradient Descent.

The following problems are taken from the projects / assignments in the edX course Python for Data Science and the coursera course Applied Machine Learning in Python (UMich). The IMDB Movie Dataset (MovieLens 20M) is used for the analysis. The dataset is downloaded from here . This dataset contains 20 million ratings and 465,000 tag applications applied to 27,000 movies by 138,000 users and was released in 4/2015. Understand the trend in average ratings for different movie genres over years (from 1995 to 2015) and Correlation between the trends for different genres (8 different genres are considered: Animation, Comedy, Romance, Thriller, Horror, Sci-Fi and Musical).

Stochastic Gradient Descent (SGD) is a very powerful technique, currently employed to optimize all deep learning models. However, the vanilla algorithm has many limitations, in particular when the system is ill-conditioned and could never find the global minimum. In this post, we're going to analyze how it works and the most important variations that can speed up the convergence in deep models. First of all, it's necessary to standardize the naming. In some books, the expression "Stochastic Gradient Descent" refers to an algorithm which operates on a batch size equal to 1, while "Mini-batch Gradient Descent" is adopted when the batch size is greater than 1.