A Spectral Algorithm for Latent Dirichlet Allocation

The problem of topic modeling can be seen as a generalization of the clustering problem, in that it posits that observations are generated due to multiple latent factors (e.g., the words in each document are generated as a mixture of several active topics, as opposed to just one). This increased representational power comes at the cost of a more challenging unsupervised learning problem of estimating the topic probability vectors (the distributions over words for each topic), when only the words are observed and the corresponding topics are hidden. We provide a simple and efficient learning procedure that is guaranteed to recover the parameters for a wide class of mixture models, including the popular latent Dirichlet allocation (LDA) model. For LDA, the procedure correctly recovers both the topic probability vectors and the prior over the topics, using only trigram statistics (i.e., third order moments, which may be estimated with documents containing just three words). The method, termed Excess Correlation Analysis (ECA), is based on a spectral decomposition of low order moments (third and fourth order) via two singular value decompositions (SVDs). Moreover, the algorithm is scalable since the SVD operations are carried out on $k\times k$ matrices, where $k$ is the number of latent factors (e.g. the number of topics), rather than in the $d$-dimensional observed space (typically $d \gg k$).Comment: Changed title to match conference version, which appears in Advances in Neural Information Processing Systems 25, 201

Deterministic Calibration and Nash Equilibrium

We provide a natural learning process in which the joint frequency of empirical play converges into the set of convex combinations of Nash equilibria. In this process, all players rationally choose their actions using a public prediction made by a deterministic, weakly calibrated algorithm. Furthermore, the public predictions used in any given round play are frequently close to some Nash equilibrium of the game

A Risk Comparison of Ordinary Least Squares vs Ridge Regression

We compare the risk of ridge regression to a simple variant of ordinary least squares, in which one simply projects the data onto a finite dimensional subspace (as specified by a Principal Component Analysis) and then performs an ordinary (un-regularized) least squares regression in this subspace. This note shows that the risk of this ordinary least squares method is within a constant factor (namely 4) of the risk of ridge regression.Comment: Appearing in JMLR 14, June 201

A Neural Networks Committee for the Contextual Bandit Problem

This paper presents a new contextual bandit algorithm, NeuralBandit, which does not need hypothesis on stationarity of contexts and rewards. Several neural networks are trained to modelize the value of rewards knowing the context. Two variants, based on multi-experts approach, are proposed to choose online the parameters of multi-layer perceptrons. The proposed algorithms are successfully tested on a large dataset with and without stationarity of rewards.Comment: 21st International Conference on Neural Information Processin

Conic Multi-Task Classification

Traditionally, Multi-task Learning (MTL) models optimize the average of task-related objective functions, which is an intuitive approach and which we will be referring to as Average MTL. However, a more general framework, referred to as Conic MTL, can be formulated by considering conic combinations of the objective functions instead; in this framework, Average MTL arises as a special case, when all combination coefficients equal 1. Although the advantage of Conic MTL over Average MTL has been shown experimentally in previous works, no theoretical justification has been provided to date. In this paper, we derive a generalization bound for the Conic MTL method, and demonstrate that the tightest bound is not necessarily achieved, when all combination coefficients equal 1; hence, Average MTL may not always be the optimal choice, and it is important to consider Conic MTL. As a byproduct of the generalization bound, it also theoretically explains the good experimental results of previous relevant works. Finally, we propose a new Conic MTL model, whose conic combination coefficients minimize the generalization bound, instead of choosing them heuristically as has been done in previous methods. The rationale and advantage of our model is demonstrated and verified via a series of experiments by comparing with several other methods.Comment: Accepted by European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases (ECMLPKDD)-201

Polymethyl Methacrylate as a Binder for Pyrotechnic Compositions

Studies on polymethyl methacrylate (PMMA) as a binder for igniter and delay compositions are reported. Igniter compositions based on magnesium and boron as fuels and potassium nitrate as oxidiser, delay compositions comprising ferrosilicon and red lead, have been investigated. These compositions were subjected to various tests, such as linear burning rate, sensitivity, calorimetric value, compatibility, pelleting properties, spark sensitivity, ignition temperatures and performance characteristics. The results indicate that the igniter compositions Mg:KNO/sub 3/:PMMA (42:50:8) and B:KNO/sub 3/:PMMA (30:70:10) as well as the delay composition comprising FeSi:Pb/sub 3/O/sub 4:PMMA (25:75:1) have improved properties and therefore could find practical applications

On Performance Evaluation of a New Liquid Propellant

A blend of 3-carene and cardanol in 70:30 weight proportion exhibits synergistic hypergolic ignition with red fuming nitric acid (RFNA) as oxidizer. Attempts have been made to evaluate this new propellant by theoretical calculationof performance parameters and verification of the results by static firing of a 10 kg thrust rocket motor around 20 atmosphers of chamber pressure. At an oxidizer-to-fuel weight ratio (O/F) of 3.34 (RFNA used had 21% N204 and 5% by weight of concentrated sulphuric acid as catalyst), the propellant produced a reasonably smooth pressure-time curve with an ignition delay of 35 milliseconds. The theoretical characteristic velocity value matched well with the experimental. No carbon residue was left in the rocket motor after firing. Specific impulse (theoretical) of the propellant has been found to be 223.8 seconds at chamber pressure, 20 atmos and exist pressure, 1 atmos

Synergistic Hypergolic Ignition of Amino End Group in Monomers and Polymers

A few monomers, oligomers and polymers with amino end groups have been discovered to undergo synergistic ignition with red fuming nitric acid (RFNA) when mixed with large quantities of magnesium powder. Aluminium powder under similar conditions does not ignite the mixture while powders of Zn, Co and Cu cause the ignition. Amongst the polymers used in the experiment commercially available nylon 6 is the most important which may be used as a binder for rocket propellant fuel grains, hypergolic with RFNA. Degree of polymerisation or the chain length of the polymers does not drastically affect the synergistic ignition of the polymer mixture with magnesium powder but high molecular weight and fully aromatised polymers like Kevlar and Nomex fail to ignite under similar conditions. Based upon the earlier work of the authors, explanations for the phenomena oberved have been provided in terms of creation of hot spots leading to ignition at the amino end groups