Latent tree models are graphical models defined on trees, in which only a subset of variables is observed. They were first discussed by Judea Pearl as tree-decomposable distributions to generalise star-decomposable distributions such as the latent class model. Latent tree models, or their submodels, are widely used in: phylogenetic analysis, network tomography, computer vision, causal modeling, and data clustering. They also contain other well-known classes of models like hidden Markov models, Brownian motion tree model, the Ising model on a tree, and many popular models used in phylogenetics. We offer here a concise introduction to the theory of latent tree models. We emphasise the role of tree metrics in the structural description of this model class, in designing learning algorithms, and in understanding fundamental limits of what and when can be learned. We present Gaussian and general Markov models as subclasses of latent tree models that admits tractable and rigorous analysis. A leaf of T is a vertex of degree one, an internal vertex is a vertex which is not a leaf, and an inner edge is an edge whose both ends are internal vertices. Given a treeT define a rooted tree as a directed graph obtained from T by picking one of its verticesr and directing all edges away fromr . The vertexr is called the root. Trees will be always leaf-labeled with the labelling set{ 1,...,m}, where m is the number of leaves. An undirected tree is trivalent if each internal vertex has degree precisely three. A rooted tree is a binary rooted tree if each internal vertex has precisely two children. In many applications rooted trees are depicted without using arrows, where direction is made implicit by drawing the root on the top and the leaves on the bottom; see Figure 1(c). Two special types of undirected trees are: a star tree with one internal vertex and a trivalent tree on four leaves called a quartet tree; see Figure 1(a) and (b). A forest is a collection of trees. Forests here are also leaf-labeled with the labelling set is{ 1,...,m}, which means that each tree in this collection is leaf-labeled and the corresponding collection of labelling sets forms a set partition of { 1,...,m}. We define three graph operations on trees (forests). Removing an edge means removing that edge from the edge set. Contracting an edge u v means removingu,v from the vertex set, adding a new vertexw and edges such thatw is adjacent to all vertices which were adjacent tou or v. Suppressing a vertex of degree two means removing that vertex and replacing the two edges incident to that vertex by a single edge. 1 2 3 4 5 1 2 3 4 (a) (b) (c) Figure 1: (a) An undirected star tree with five leaves, (b) a quartet tree, (c) a binary rooted tree.

Lecture 1 of Tim Roughgarden's Algorithmic Game Theory class at Stanford (Autumn 2013) Class description: Topics at the interface of computer science and game theory such as: algorithmic mechanism design; combinatorial auctions; computation of Nash equilibria and relevant complexity theory; congestion and potential games; cost sharing; game theory and the Internet; matching markets; network formation; online learning algorithms; price of anarchy; prior-free auctions; selfish routing; sponsored search.

Special note: we're teaching a fully updated part 1, in person, for seven weeks from Oct 30, 2017, at the USF Data Institute. See the course page for details and application form. Part 1 of the course has now been viewed by tens of thousands of students, introducing them to nearly all of today's best practices in deep learning, and providing many hours of hands-on practical coding exercises. We have collected some stories from graduates of part 1 on our testimonials page. Today, we are launching Part 2: Cutting Edge Deep Learning for Coders.

Welcome to a new section in our Machine Learning Tutorial series: Deep Learning with Neural Networks and TensorFlow. The artificial neural network is a biologically-inspired methodology to conduct machine learning, intended to mimic your brain (a biological neural network). The Artificial Neural Network, which I will now just refer to as a neural network, is not a new concept. The idea has been around since the 1940's, and has had a few ups and downs, most notably when compared against the Support Vector Machine (SVM). For example, the Neural Network was popularized up until the mid 90s when it was shown that the SVM, using a new-to-the-public (the technique itself was thought up long before it was actually put to use) technique, the "Kernel Trick," was capable of working with non-linearly separable datasets.

Discover how to use Python--and some essential machine learning concepts--to build programs that can make recommendations. She helps you learn the concepts behind how recommendation systems work by taking you through a series of examples and exercises. Once you're familiar with the underlying concepts, Lillian explains how to apply statistical and machine learning methods to construct your own recommenders. She demonstrates how to build a popularity-based recommender using the Pandas library, how to recommend similar items based on correlation, and how to deploy various machine learning algorithms to make recommendations. At the end of the course, she shows how to evaluate which recommender performed the best.

The other day I was reading an article on how AI has progressed so far and where it is going. I was awestruck and had a hard time digesting the picture the author drew on possibilities in the future. Here is how I reacted. "A surgeon could control a machine scalpel with her motor cortex instead of holding one in her hand, and she could receive sensory input from that scalpel so that it would feel like an 11th finger to her. So it would be as if one of her fingers was a scalpel and she could do the surgery without holding any tools, giving her much finer control over her incisions. An inexperienced surgeon performing a tough operation could bring a couple of her mentors into the scene as she operates to watch her work through her eyes and think instructions or advice to her. And if something goes really wrong, one of them could "take the wheel" and connect their motor cortex to her outputs to take control of her hands."

In this work, we design and evaluate a computational learning model that enables a human-robot team to co-develop joint strategies for performing novel tasks that require coordination. The joint strategies are learned through "perturbation training," a human team-training strategy that requires team members to practice variations of a given task to help their team generalize to new variants of that task. We formally define the problem of human-robot perturbation training and develop and evaluate the first end-to-end framework for such training, which incorporates a multi-agent transfer learning algorithm, human-robot co-learning framework and communication protocol. Our transfer learning algorithm, Adaptive Perturbation Training (AdaPT), is a hybrid of transfer and reinforcement learning techniques that learns quickly and robustly for new task variants. We empirically validate the benefits of AdaPT through comparison to other hybrid reinforcement and transfer learning techniques aimed at transferring knowledge from multiple source tasks to a single target task. We also demonstrate that AdaPT's rapid learning supports live interaction between a person and a robot, during which the human-robot team trains to achieve a high level of performance for new task variants. We augment AdaPT with a co-learning framework and a computational bi-directional communication protocol so that the robot can co-train with a person during live interaction. Results from large-scale human subject experiments (n=48) indicate that AdaPT enables an agent to learn in a manner compatible with a human's own learning process, and that a robot undergoing perturbation training with a human results in a high level of team performance. Finally, we demonstrate that human-robot training using AdaPT in a simulation environment produces effective performance for a team incorporating an embodied robot partner.

Last Friday, we mentioned how Google's artificial intelligence software DeepMind has the ability to teach itself many things. It can teach itself how to walk, jump and run. Or defeat the world's best player of the Chinese strategy game, Go. The science of teaching computers how to do things is called Deep Learning. Offered through Udacity, the course is taught by Vincent Vanhoucke, the technical lead in Google's Brain team.

FOR a ten-year-old, Amartya is a thoughtful chap. One Monday morning at the Khan Lab School (KLS) in Mountain View, California, he explains that his maths is "pretty strong" but he needs to work on his writing. Not to worry, though; Amartya has a plan. He will practise grammar online, book a slot with an English teacher and consult his mentor. Later he will e-mail your correspondent to ask for help, too. This is the sort of pluck KLS produces. Its pupils do not have homework or report cards or spend all day in classrooms.