Optimal transport (OT) is a powerful tool for measuring the distance between two defined probability distributions. In this paper, we develop a new manifold named the coupling matrix manifold (CMM), where each point on CMM can be regarded as the transportation plan of the OT problem. We firstly explore the Riemannian geometry of CMM with the metric expressed by the Fisher information. These geometrical features of CMM have paved the way for developing numerical Riemannian optimization algorithms such as Riemannian gradient descent and Riemannian trust-region algorithms, forming a uniform optimization method for all types of OT problems. The proposed method is then applied to solve several OT problems studied by previous literature. The results of the numerical experiments illustrate that the optimization algorithms that are based on the method proposed in this paper are comparable to the classic ones, for example, the Sinkhorn algorithm, while outperforming other state-of-the-art algorithms without considering the geometry information, especially in the case of non-entropy optimal transport.

Multi-view time series classification aims to fuse the distinctive temporal information from different views to further enhance the classification performance. Existing methods mainly focus on fusing multi-view features at an early stage ( e.g., learning a common representation shared by multiple views). However, these early fusion methods may not fully exploit the view-specific distinctive patterns in high-dimension time series data. Moreover, the intra-view and interview label correlations, which are critical for multi-view classification, are usually ignored in previous works. In this paper, we propose a Global-Local Correlative Channel-A ware Fusion (GLCCF) model to address the aforementioned issues. Particularly, our model extracts global and local temporal patterns by a two-stream structure encoder, captures the intra-view and interview label correlations by constructing a graph based correlation matrix, and extracts the cross-view global patterns via a learnable channel-aware late fusion mechanism, which could be effectively implemented with a convo-lutional neural network. Extensive experiments on two real-world datasets demonstrate the superiority of our approach over the state-of-the-art methods. An ablation study is further provided to show the effectiveness of each model component. Introduction Time series classification has attracted increasing attention recently since temporal data contains more dynamic patterns which cannot be discovered easily.

In many real-world applications of machine learning, data are distributed across many clients and cannot leave the devices they are stored on. Furthermore, each client's data, computational resources and communication constraints may be very different. This setting is known as federated learning, in which privacy is a key concern. Differential privacy is commonly used to provide mathematical privacy guarantees. This work, to the best of our knowledge, is the first to consider federated, differentially private, Bayesian learning. We build on Partitioned Variational Inference (PVI) which was recently developed to support approximate Bayesian inference in the federated setting. We modify the client-side optimisation of PVI to provide an (${\epsilon}$, ${\delta}$)-DP guarantee. We show that it is possible to learn moderately private logistic regression models in the federated setting that achieve similar performance to models trained non-privately on centralised data.

Graphical causal inference as pioneered by Judea Pearl arose from research on artificial intelligence (AI), and for a long time had little connection to the field of machine learning. This article discusses where links have been and should be established, introducing key concepts along the way. It argues that the hard open problems of machine learning and AI are intrinsically related to causality, and explains how the field is beginning to understand them.

Suffice it to say that they are a form of non-linear regression tool whose underlying design found inspiration in a simplification of the basic architecture of the human brain. Many of the great advances that we have experienced in Machine Learning over the last few years make use of neural networks. The basic algorithm has been around for decades -- but it has come into its own as processing power and data availability have steadily increased. For this project we implemented our neural network in Python using the popular TensorFlow library from Google. The characteristics of our neural network, and in particular its complexity, were chosen to balance precision and generalization.

What is Confusion Matrix and Advanced Classification Metrics? After data preparation and model training, there is model evaluat... Root Mean Square Error (RMSE) How to calculate Root-Mean-Square Error? This post will cover most common ways to evaluate the regression model. The idea of reg... Machine Learning Process Simple Picture of Machine Learning Modelling Process Learning machine is computer algorithm to search patterns in massive data.... Regression Techniques Regression Techniques By Their Machine Learning Families Several Machine Learning (ML) algorithms and families are out t... Research Paper on Machine Learning Research Papers on Classifiers and Regression Models In this article, I am going to write on two most important research papers... It's Easy to Learn MapReduce process In this article, I have tried to cover MapReduce process by explaining Map and Reduce cycl... Machine Learning Overview Machine Learning Overview For easy understanding of ML overview, this post shows the cheat sheet of types of ML with some algorith... What is Confusion Matrix and Advanced Classification Metrics? After data preparation and model training, there is model evaluat... What is Confusion Matrix and Advanced Classification Metrics?

Learn how to run Multiple Linear Regression Analysis using Python from scratch! Learn the process of Machine Learning and all the tasks / steps you must undertake. Then, learn how to apply them using some dummy data and a Multiple Linear Regression Algorithm in Python using scikit (SKLearn) library. How to use our Linear Regression model How to download and install Python through Anaconda: https://youtu.be/__8BK62j-bw

The multidisciplinary field of data science is concerned with extracting insights from data using a diverse set of computational methodologies, theories, and technologies (Blei and Smyth 2017). Within data science, there are two competing scientific philosophies: classical statistics and machine learning (Breiman 2001b). Classical statistics aims to formalise relationships between dependent and independent variables based on a clearly defined set of assumptions from which mathematical models are parametrised. The aim is to derive meaningful statistical inference (properties of an underlying probability distribution) for the measured variables, assuming that the observed data is sampled from a larger population. Conversely, machine learning uses ad-hoc computational algorithms that iteratively optimise (or'learn') without necessarily relying on any formal statistical assumptions (Bishop 1995).

Figure 1: Illustration of the meta-learning process as applied to the task of personalized next-word prediction. Here each mobile device corresponds to a different next-word prediction task, with the test-task not seen during meta-training (Step 1). In the classical machine learning setup, we aim to learn a single model for a single task given many training samples from the same distribution. However, in many practical applications, we are in fact exposed to several distinct yet related tasks that have only a few examples each. Because the data now come from different training distributions, simply learning a single global model, e.g., via stochastic gradient descent (SGD), may result in poor performance on each task.

Smoothing splines provide a powerful and flexible means for nonparametric estimation and inference. With a cubic time complexity, fitting smoothing spline models to large data is computationally prohibitive. In this paper, we use the theoretical optimal eigenspace to derive a low rank approximation of the smoothing spline estimates. We develop a method to approximate the eigensystem when it is unknown and derive error bounds for the approximate estimates. The proposed methods are easy to implement with existing software. Extensive simulations show that the new methods are accurate, fast, and compares favorably against existing methods.