Spectral dimensionality reduction for HMMs

Hidden Markov Models (HMMs) can be accurately approximated using co-occurrence frequencies of pairs and triples of observations by using a fast spectral method in contrast to the usual slow methods like EM or Gibbs sampling. We provide a new spectral method which significantly reduces the number of model parameters that need to be estimated, and generates a sample complexity that does not depend on the size of the observation vocabulary. We present an elementary proof giving bounds on the relative accuracy of probability estimates from our model. (Correlaries show our bounds can be weakened to provide either L1 bounds or KL bounds which provide easier direct comparisons to previous work.) Our theorem uses conditions that are checkable from the data, instead of putting conditions on the unobservable Markov transition matrix

Bridging the Usability Gap: Theoretical and Methodological Advances for Spectral Learning of Hidden Markov Models

The Baum-Welch (B-W) algorithm is the most widely accepted method for inferring hidden Markov models (HMM). However, it is prone to getting stuck in local optima, and can be too slow for many real-time applications. Spectral learning of HMMs (SHMMs), based on the method of moments (MOM) has been proposed in the literature to overcome these obstacles. Despite its promises, asymptotic theory for SHMM has been elusive, and the long-run performance of SHMM can degrade due to unchecked propogation of error. In this paper, we (1) provide an asymptotic distribution for the approximate error of the likelihood estimated by SHMM, and (2) propose a novel algorithm called projected SHMM (PSHMM) that mitigates the problem of error propogation, and (3) develop online learning variantions of both SHMM and PSHMM that accommodate potential nonstationarity. We compare the performance of SHMM with PSHMM and estimation through the B-W algorithm on both simulated data and data from real world applications, and find that PSHMM not only retains the computational advantages of SHMM, but also provides more robust estimation and forecasting

When black box algorithms are (not) appropriate: a principled prediction-problem ontology

In the 1980s a new, extraordinarily productive way of reasoning about algorithms emerged. Though this type of reasoning has come to dominate areas of data science, it has been under-discussed and its impact under-appreciated. For example, it is the primary way we reason about "black box" algorithms. In this paper we analyze its current use (i.e., as "the common task framework") and its limitations; we find a large class of prediction-problems are inappropriate for this type of reasoning. Further, we find the common task framework does not provide a foundation for the deployment of an algorithm in a real world situation. Building off of its core features, we identify a class of problems where this new form of reasoning can be used in deployment. We purposefully develop a novel framework so both technical and non-technical people can discuss and identify key features of their prediction problem and whether or not it is suitable for this new kind of reasoning

Nonlinear Permuted Granger Causality

Granger causal inference is a contentious but widespread method used in fields ranging from economics to neuroscience. The original definition addresses the notion of causality in time series by establishing functional dependence conditional on a specified model. Adaptation of Granger causality to nonlinear data remains challenging, and many methods apply in-sample tests that do not incorporate out-of-sample predictability, leading to concerns of model overfitting. To allow for out-of-sample comparison, a measure of functional connectivity is explicitly defined using permutations of the covariate set. Artificial neural networks serve as featurizers of the data to approximate any arbitrary, nonlinear relationship, and consistent estimation of the variance for each permutation is shown under certain conditions on the featurization process and the model residuals. Performance of the permutation method is compared to penalized variable selection, naive replacement, and omission techniques via simulation, and it is applied to neuronal responses of acoustic stimuli in the auditory cortex of anesthetized rats. Targeted use of the Granger causal framework, when prior knowledge of the causal mechanisms in a dataset are limited, can help to reveal potential predictive relationships between sets of variables that warrant further study

Switching to smokeless tobacco as a smoking cessation method: evidence from the 2000 National Health Interview Survey

<p>Abstract</p> <p>Background</p> <p>Although smokeless tobacco (ST) use has played a major role in the low smoking prevalence among Swedish men, there is little information at the population level about ST as a smoking cessation aid in the U.S.</p> <p>Methods</p> <p>We used the 2000 National Health Interview Survey to derive population estimates for the number of smokers who had tried twelve methods in their most recent quit attempt, and for the numbers and proportions who were former or current smokers at the time of the survey.</p> <p>Results</p> <p>An estimated 359,000 men switched to smokeless tobacco in their most recent quit attempt. This method had the highest proportion of successes among those attempting it (73%), representing 261,000 successful quitters (switchers). In comparison, the nicotine patch was used by an estimated 2.9 million men in their most recent quit attempt, and almost one million (35%) were former smokers at the time of the survey. Of the 964,000 men using nicotine gum, about 323,000 (34%) became former smokers. Of the 98,000 men who used the nicotine inhaler, 27,000 quit successfully (28%). None of the estimated 14,000 men who tried the nicotine nasal spray became former smokers.</p> <p>Forty-two percent of switchers also reported quitting smoking all at once, which was higher than among former smokers who used medications (8–19%). Although 40% of switchers quit smoking less than 5 years before the survey, 21% quit over 20 years earlier. Forty-six percent of switchers were current ST users at the time of the survey.</p> <p>Conclusion</p> <p>Switching to ST compares very favorably with pharmaceutical nicotine as a quit-smoking aid among American men, despite the fact that few smokers know that the switch provides almost all of the health benefits of complete tobacco abstinence. The results of this study show that tobacco harm reduction is a viable cessation option for American smokers.</p

Tobacco harm reduction: an alternative cessation strategy for inveterate smokers

According to the Centers for Disease Control and Prevention, about 45 million Americans continue to smoke, even after one of the most intense public health campaigns in history, now over 40 years old. Each year some 438,000 smokers die from smoking-related diseases, including lung and other cancers, cardiovascular disorders and pulmonary diseases. Many smokers are unable – or at least unwilling – to achieve cessation through complete nicotine and tobacco abstinence; they continue smoking despite the very real and obvious adverse health consequences. Conventional smoking cessation policies and programs generally present smokers with two unpleasant alternatives: quit, or die. A third approach to smoking cessation, tobacco harm reduction, involves the use of alternative sources of nicotine, including modern smokeless tobacco products. A substantial body of research, much of it produced over the past decade, establishes the scientific and medical foundation for tobacco harm reduction using smokeless tobacco products. This report provides a description of traditional and modern smokeless tobacco products, and of the prevalence of their use in the United States and Sweden. It reviews the epidemiologic evidence for low health risks associated with smokeless use, both in absolute terms and in comparison to the much higher risks of smoking. The report also describes evidence that smokeless tobacco has served as an effective substitute for cigarettes among Swedish men, who consequently have among the lowest smoking-related mortality rates in the developed world. The report documents the fact that extensive misinformation about ST products is widely available from ostensibly reputable sources, including governmental health agencies and major health organizations. The American Council on Science and Health believes that strong support of tobacco harm reduction is fully consistent with its mission to promote sound science in regulation and in public policy, and to assist consumers in distinguishing real health threats from spurious health claims. As this report documents, there is a strong scientific and medical foundation for tobacco harm reduction, and it shows great potential as a public health strategy to help millions of smokers

Change Point Detection with Conceptors

Offline change point detection retrospectively locates change points in a time series. Many nonparametric methods that target i.i.d. mean and variance changes fail in the presence of nonlinear temporal dependence, and model based methods require a known, rigid structure. For the at most one change point problem, we propose use of a conceptor matrix to learn the characteristic dynamics of a baseline training window with arbitrary dependence structure. The associated echo state network acts as a featurizer of the data, and change points are identified from the nature of the interactions between the features and their relationship to the baseline state. This model agnostic method can suggest potential locations of interest that warrant further study. We prove that, under mild assumptions, the method provides a consistent estimate of the true change point, and quantile estimates are produced via a moving block bootstrap of the original data. The method is evaluated with clustering metrics and Type 1 error control on simulated data, and applied to publicly available neural data from rats experiencing bouts of non-REM sleep prior to exploration of a radial maze. With sufficient spacing, the framework provides a simple extension to the sparse, multiple change point problem

Socio-demographic, lifestyle and health characteristics among snus users and dual tobacco users in Stockholm County, Sweden

<p>Abstract</p> <p>Background</p> <p>Socio-demographic and lifestyle characteristics of snus users have not been systematically described. Such knowledge is pivotal for tobacco control efforts and for the assessment of health effects of snus use.</p> <p>Methods</p> <p>A cross-sectional study was conducted, based on the Stockholm Public Health Survey, including a population-based sample of 34,707 men and women aged 18-84 years. We examined how socio-demographic, lifestyle and health-related characteristics were associated with the prevalence of current daily snus use, smoking and dual tobacco use. Logistic regression was used to calculate odds ratios of prevalence (ORs) and 95% confidence intervals (CIs).</p> <p>Results</p> <p>Low educational level (OR = 1.60, CI = 1.41-1.81 and OR = 1.49, CI = 1.17-1.89, for men and women respectively), as well as occupational class and low income were associated with snus use. Some unfavourable lifestyle characteristics, including risky alcohol consumption (males: OR = 1.81, CI = 1.63-2.02; females: OR = 1.79, CI = 1.45-2.20), binge drinking and low consumption of fruit and vegetables were also associated with snus use. In contrast, physical inactivity and overweight/obesity were not, nor was perceived health. The prevalence of smoking followed steeper gradients for social as well as lifestyle characteristics. Overweight and obese men were however less often smokers. Perceived poor general health and psychological distress were highly related to smoking. Social disadvantage, as well as unhealthy lifestyle and self-reported poor health were strongly associated with dual use. There were limited differences between men and women.</p> <p>Conclusions</p> <p>The social, lifestyle and health profiles of exclusive snus users in Stockholm County are less favourable than those of non-users of tobacco, but more advantageous than those of exclusive smokers. This knowledge should guide tobacco control measures as well as the interpretation of health risks linked to snus use.</p