Regularization is one of the crucial ingredients of deep learning, yet the term regularization has various definitions, and regularization methods are often studied separately from each other. In our work we present a systematic, unifying taxonomy to categorize existing methods. We distinguish methods that affect data, network architectures, error terms, regularization terms, and optimization procedures. We do not provide all details about the listed methods; instead, we present an overview of how the methods can be sorted into meaningful categories and sub-categories. This helps revealing links and fundamental similarities between them. Finally, we include practical recommendations both for users and for developers of new regularization methods.

Stochastic gradient descent in continuous time (SGDCT) provides a computationally efficient method for the statistical learning of continuous-time models, which are widely used in science, engineering, and finance. The SGDCT algorithm follows a (noisy) descent direction along a continuous stream of data. SGDCT performs an online parameter update in continuous time, with the parameter updates $\theta_t$ satisfying a stochastic differential equation. We prove that $\lim_{t \rightarrow \infty} \nabla \bar g(\theta_t) = 0$ where $\bar g$ is a natural objective function for the estimation of the continuous-time dynamics. The convergence proof leverages ergodicity by using an appropriate Poisson equation to help describe the evolution of the parameters for large times. SGDCT can also be used to solve continuous-time optimization problems, such as American options. For certain continuous-time problems, SGDCT has some promising advantages compared to a traditional stochastic gradient descent algorithm. As an example application, SGDCT is combined with a deep neural network to price high-dimensional American options (up to 100 dimensions).

Given only information in the form of similarity triplets "Object A is more similar to object B than to object C" about a data set, we propose two ways of defining a kernel function on the data set. While previous approaches construct a low-dimensional Euclidean embedding of the data set that reflects the given similarity triplets, we aim at defining kernel functions that correspond to high-dimensional embeddings. These kernel functions can subsequently be used to apply any kernel method to the data set.

Today we are demo-ing the h2o package for machine learning on time series data. Every day this week we are demoing an R package: tidyquant (Monday), timetk (Tuesday), sweep (Wednesday), tibbletime (Thursday) and h2o (Friday)! We'll give you intel on what you need to know about these packages to go from zero to hero. Today you'll see how we can use timetk h2o to get really accurate time series forecasts. The h2o package is a product offered by H2O.ai that contains a number of cutting edge machine learning algorithms, performance metrics, and auxiliary functions to make machine learning both powerful and easy.

Regression is arguably the workhorse of statistics. Despite its popularity, however, it may also be the most misunderstood. The answer might surprise you: There is no such thing as Regression. The Dependent Variable is something you want to predict or explain. In a Marketing Research context it might be Purchase Interest measured on a 0-10 rating scale.

Numerical computation, knowledge discovery and statistical data analysis integrated with powerful 2D and 3D graphics for visualization are the key topics of this book. The Python code examples powered by the Java platform can easily be transformed to other programming languages, such as Java, Groovy, Ruby and BeanShell. This book equips the reader with a computational platform which, unlike other statistical programs, is not limited by a single programming language. The author focuses on practical programming aspects and covers a broad range of topics, from basic introduction to the Python language on the Java platform (Jython), to descriptive statistics, symbolic calculations, neural networks, non-linear regression analysis and many other data-mining topics. He discusses how to find regularities in real-world data, how to classify data, and how to process data for knowledge discoveries.

We propose a new localized inference algorithm for answering marginalization queries in large graphical models with the correlation decay property. Given a query variable and a large graphical model, we define a much smaller model in a local region around the query variable in the target model so that the marginal distribution of the query variable can be accurately approximated. We introduce two approximation error bounds based on the Dobrushin's comparison theorem and apply our bounds to derive a greedy expansion algorithm that efficiently guides the selection of neighbor nodes for localized inference. We verify our theoretical bounds on various datasets and demonstrate that our localized inference algorithm can provide fast and accurate approximation for large graphical models.

It's time to write our first classifier. This is a milestone if you're new to machine learning. We'll start with our code from episode #4 and comment out the classifier we imported.

"Our single XGBoost model can get to the top three! Our final model just averaged XGBoost models with different random seeds." With entire blogs dedicated to how the sole application of XGBoost can propel one's ranking on Kaggle competitions, it is time we delved deeper into the concepts of XGBoost. Bagging algorithms control for high variance in a model. However, boosting algorithms are considered more effective as they deal with both bias as well as variance (the bias-variance trade-off).

DBSCAN is a different type of clustering algorithm with some unique advantages. As the name indicates, this method focuses more on the proximity and density of observations to form clusters. This is very different from KMeans, where an observation becomes a part of cluster represented by nearest centroid. DBSCAN clustering can identify outliers, observations which won't belong to any cluster. Since DBSCAN clustering identifies the number of clusters as well, it is very useful with unsupervised learning of the data when we don't know how many clusters could be there in the data.