In application domains such as healthcare, we want accurate predictive models that are also causally interpretable. In pursuit of such models, we propose a causal regularizer to steer predictive models towards causally-interpretable solutions and theoretically study its properties. In a large-scale analysis of Electronic Health Records (EHR), our causally-regularized model outperforms its L1-regularized counterpart in causal accuracy and is competitive in predictive performance. We perform non-linear causality analysis by causally regularizing a special neural network architecture. We also show that the proposed causal regularizer can be used together with neural representation learning algorithms to yield up to 20% improvement over multilayer perceptron in detecting multivariate causation, a situation common in healthcare, where many causal factors should occur simultaneously to have an effect on the target variable.

The problem of on-line off-policy evaluation (OPE) has been actively studied in the last decade due to its importance both as a stand-alone problem and as a module in a policy improvement scheme. However, most Temporal Difference (TD) based solutions ignore the discrepancy between the stationary distribution of the behavior and target policies and its effect on the convergence limit when function approximation is applied. In this paper we propose the Consistent Off-Policy Temporal Difference (COP-TD($\lambda$, $\beta$)) algorithm that addresses this issue and reduces this bias at some computational expense. We show that COP-TD($\lambda$, $\beta$) can be designed to converge to the same value that would have been obtained by using on-policy TD($\lambda$) with the target policy. Subsequently, the proposed scheme leads to a related and promising heuristic we call log-COP-TD($\lambda$, $\beta$). Both algorithms have favorable empirical results to the current state of the art on-line OPE algorithms. Finally, our formulation sheds some new light on the recently proposed Emphatic TD learning.

We introduce a simple permutation equivariant layer for deep learning with set structure.This type of layer, obtained by parameter-sharing, has a simple implementation and linear-time complexity in the size of each set. We use deep permutation-invariant networks to perform point-could classification and MNIST-digit summation, where in both cases the output is invariant to permutations of the input. In a semi-supervised setting, where the goal is make predictions for each instance within a set, we demonstrate the usefulness of this type of layer in set-outlier detection as well as semi-supervised learning with clustering side-information.

Clustering is the grouping of objects together so that objects belonging in the same group (cluster) are more similar to each other than those in other groups (clusters). In this intro cluster analysis tutorial, we'll check out a few algorithms in Python so you can get a basic understanding of the fundamentals of clustering on a real dataset. For the clustering problem, we will use the famous Zachary's Karate Club dataset. The story behind the data set is quite simple: There was a Karate Club that had an administrator "John A" and an instructor "Mr. Then a conflict arose between them, causing the students (Nodes) to split into two groups.

Imagine a case - if there is no straight line (or hyperplane) which can separate two classes? In the image shown below, there is a circle in 2D with red and blue data points all over it such that adjacent data points are of different colors. SVM handles the above case by using a kernel function to handle non-linear separable data. It is explained in the next section.

Network embeddings have become very popular in learning effective feature representations of networks. Motivated by the recent successes of embeddings in natural language processing, researchers have tried to find network embeddings in order to exploit machine learning algorithms for mining tasks like node classification and edge prediction. However, most of the work focuses on finding distributed representations of nodes, which are inherently ill-suited to tasks such as community detection which are intuitively dependent on subgraphs. Here, we propose sub2vec, an unsupervised scalable algorithm to learn feature representations of arbitrary subgraphs. We provide means to characterize similarties between subgraphs and provide theoretical analysis of sub2vec and demonstrate that it preserves the so-called local proximity. We also highlight the usability of sub2vec by leveraging it for network mining tasks, like community detection. We show that sub2vec gets significant gains over state-of-the-art methods and node-embedding methods. In particular, sub2vec offers an approach to generate a richer vocabulary of features of subgraphs to support representation and reasoning.

We present a scalable approach for semi-supervised learning on graph-structured data that is based on an efficient variant of convolutional neural networks which operate directly on graphs. We motivate the choice of our convolutional architecture via a localized first-order approximation of spectral graph convolutions. Our model scales linearly in the number of graph edges and learns hidden layer representations that encode both local graph structure and features of nodes. In a number of experiments on citation networks and on a knowledge graph dataset we demonstrate that our approach outperforms related methods by a significant margin.

Partial Least Squares (PLS) methods have been heavily exploited to analyse the association between two blocs of data. These powerful approaches can be applied to data sets where the number of variables is greater than the number of observations and in presence of high collinearity between variables. Different sparse versions of PLS have been developed to integrate multiple data sets while simultaneously selecting the contributing variables. Sparse modelling is a key factor in obtaining better estimators and identifying associations between multiple data sets. The cornerstone of the sparsity version of PLS methods is the link between the SVD of a matrix (constructed from deflated versions of the original matrices of data) and least squares minimisation in linear regression. We present here an accurate description of the most popular PLS methods, alongside their mathematical proofs. A unified algorithm is proposed to perform all four types of PLS including their regularised versions. Various approaches to decrease the computation time are offered, and we show how the whole procedure can be scalable to big data sets.

Stochastic Neighbor Embedding and its variants are widely used dimensionality reduction techniques -- despite their popularity, no theoretical results are known. We prove that the optimal SNE embedding of well-separated clusters from high dimensions to any Euclidean space R^d manages to successfully separate the clusters in a quantitative way. The result also applies to a larger family of methods including a variant of t-SNE.

Stochastic gradient descent (SGD) still is the workhorse for many practical problems. However, it converges slow, and can be difficult to tune. It is possible to precondition SGD to accelerate its convergence remarkably. But many attempts in this direction either aim at solving specialized problems, or result in significantly more complicated methods than SGD. This paper proposes a new method to estimate a preconditioner such that the amplitudes of perturbations of preconditioned stochastic gradient match that of the perturbations of parameters to be optimized in a way comparable to Newton method for deterministic optimization. Unlike the preconditioners based on secant equation fitting as done in deterministic quasi-Newton methods, which assume positive definite Hessian and approximate its inverse, the new preconditioner works equally well for both convex and non-convex optimizations with exact or noisy gradients. When stochastic gradient is used, it can naturally damp the gradient noise to stabilize SGD. Efficient preconditioner estimation methods are developed, and with reasonable simplifications, they are applicable to large scaled problems. Experimental results demonstrate that equipped with the new preconditioner, without any tuning effort, preconditioned SGD can efficiently solve many challenging problems like the training of a deep neural network or a recurrent neural network requiring extremely long term memories.