General adjoint-differentiated Laplace approximation

The hierarchical prior used in Latent Gaussian models (LGMs) induces a posterior geometry prone to frustrate inference algorithms. Marginalizing out the latent Gaussian variable using an integrated Laplace approximation removes the offending geometry, allowing us to do efficient inference on the hyperparameters. To use gradient-based inference we need to compute the approximate marginal likelihood and its gradient. The adjoint-differentiated Laplace approximation differentiates the marginal likelihood and scales well with the dimension of the hyperparameters. While this method can be applied to LGMs with any prior covariance, it only works for likelihoods with a diagonal Hessian. Furthermore, the algorithm requires methods which compute the first three derivatives of the likelihood with current implementations relying on analytical derivatives. I propose a generalization which is applicable to a broader class of likelihoods and does not require analytical derivatives of the likelihood. Numerical experiments suggest the added flexibility comes at no computational cost: on a standard LGM, the new method is in fact slightly faster than the existing adjoint-differentiated Laplace approximation. I also apply the general method to an LGM with an unconventional likelihood. This example highlights the algorithm's potential, as well as persistent challenges

Vibrotactile pattern recognition on the torso : effects of concurrent activities

Thesis (S.B.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2007.Includes bibliographical references (leaf 25).Vibrotactile displays have been created to aid vision or hearing through the sense of touch. These displays communicate with the user to provide information. The focus of this thesis was to determine how concurrent activity affects vibrotactile signal recognition. An overall accuracy recognition rate of 90% or greater was desired from each of the signals in the each of the tasks. The first experiment asked subjects to wear the tactile display and walk while responding to signals. The results indicated that most of the subjects were able to recognize the patterns. The overall mean correct response rate was 92% and then when the subjects were asked to jog, they correctly identified the patterns 91% of the time. After determining the success rates from the first experiment, a second set of subjects were asked to concentrate on an internet game while responding to signals. The data from this experiment had an overall mean correct response rate of 93%. The results from this experiment further indicate that subjects can still receive communications while participating in other activities. The results also lead to specific conclusions about the patterns used and their ability to be identified with concurrent activity where some patterns are more easily received than others. By understanding how these patterns are recognized by humans, we can better develop patterns to communicate through tactile devices.by Christa M. Margossian.S.B

Study of the Need for Free Preventive Examinations for Cervical Cancer

Aim: The aim of this article is to investigate the need for free preventive examinations for cervical cancer.Materials and Methods: A total of 120 women were randomly selected. The study was conducted in the period May 20-30, 2018 at the Complex Oncology Center - Shumen. The study used survey methods (direct, group, anonymous poll), literature analysis, documentary method. Data was processed by statistical and graphical analysis.Results and Discussion:All respondents said that free examinations would increase cervical cancer prevention, because the most vulnerable age group is between 30 and 50 years. It turned out that some of the respondents were suffering from a malignant neoplasm of the cervix, and have undergone chemotherapy, radiotherapy, and hormone therapy. This was a treatment, which has led to severe economic consequences in the financial situation of the family, which in turn reduced the possibility of follow-up preventive examinations. Some of the respondents were of low health culture and were unaware of the importance of prevention and the risk of the disease. This is a disease that has more and more victims at a young age due to the low economic standard of living, health culture, and the need for preventive examinations in risk groups. Organized free examinations enable a large proportion of the low-income population to benefit from this kind of medical examination

Amortized Variational Inference: When and Why?

Amortized variational inference (A-VI) is a method for approximating the intractable posterior distributions that arise in probabilistic models. The defining feature of A-VI is that it learns a global inference function that maps each observation to its local latent variable's approximate posterior. This stands in contrast to the more classical factorized (or mean-field) variational inference (F-VI), which directly learns the parameters of the approximating distribution for each latent variable. In deep generative models, A-VI is used as a computational trick to speed up inference for local latent variables. In this paper, we study A-VI as a general alternative to F-VI for approximate posterior inference. A-VI cannot produce an approximation with a lower Kullback-Leibler divergence than F-VI's optimal solution, because the amortized family is a subset of the factorized family. Thus a central theoretical problem is to characterize when A-VI still attains F-VI's optimal solution. We derive conditions on both the model and the inference function under which A-VI can theoretically achieve F-VI's optimum. We show that for a broad class of hierarchical models, including deep generative models, it is possible to close the gap between A-VI and F-VI. Further, for an even broader class of models, we establish when and how to expand the domain of the inference function to make amortization a feasible strategy. Finally, we prove that for certain models -- including hidden Markov models and Gaussian processes -- A-VI cannot match F-VI's solution, no matter how expressive the inference function is. We also study A-VI empirically. On several examples, we corroborate our theoretical results and investigate the performance of A-VI when varying the complexity of the inference function. When the gap between A-VI and F-VI can be closed, we find that the required complexity of the function need not scale with the number of observations, and that A-VI often converges faster than F-VI

Bayesian workflow for disease transmission modeling in Stan

This tutorial shows how to build, fit, and criticize disease transmission models in Stan, and should be useful to researchers interested in modeling the SARS-CoV-2 pandemic and other infectious diseases in a Bayesian framework. Bayesian modeling provides a principled way to quantify uncertainty and incorporate both data and prior knowledge into the model estimates. Stan is an expressive probabilistic programming language that abstracts the inference and allows users to focus on the modeling. As a result, Stan code is readable and easily extensible, which makes the modeler's work more transparent. Furthermore, Stan's main inference engine, Hamiltonian Monte Carlo sampling, is amiable to diagnostics, which means the user can verify whether the obtained inference is reliable. In this tutorial, we demonstrate how to formulate, fit, and diagnose a compartmental transmission model in Stan, first with a simple Susceptible-Infected-Recovered (SIR) model, then with a more elaborate transmission model used during the SARS-CoV-2 pandemic. We also cover advanced topics which can further help practitioners fit sophisticated models; notably, how to use simulations to probe the model and priors, and computational techniques to scale-up models based on ordinary differential equations

Evaluation of SpermTracker paper and spray for the visualization of seminal stains

In a single day’s work in the serology unit of a forensic laboratory, an analyst may encounter a wide array of evidentiary items ranging in size, shape, color, texture, porosity etc. When an item is received, the analyst must first decipher what biological fluid is suspected to be present, and then how to analyze the item for that fluid. Blood, saliva, and semen are all common body fluids that may be detected in everyday casework. The identification of semen plays a key role in the investigation of a sexual assault case. When an item is received for analysis, semen stains may be undetectable to the naked eye, so a proper visualization method is crucial. Throughout this study, two presumptive tests for semen, STK® SpermTracker-Lab and STK® SpermTracker-Spray were compared to each other and the existing Acid Phosphatase Spot Test (AP-Spot) to assess their efficacy for visualizing seminal stains. Six different commonly encountered substrates varying in color, texture, and porosity were tested. Four semen dilutions were added in triplicate to each of the six substrates, to aid in the evaluation of each test’s sensitivity. A total of 324 presumptive tests for seminal stains were completed and examined both with the naked eye and with the aid of an alternate light source. STK® SpermTracker-Lab proved to be the most sensitive, closely followed by the AP-Spot test. STK® SpermTracker-Spray was least effective at detecting semen stains, however, many of the negative results obtained with STK®-Spray were on porous substrates that the manufacturer does not recommend for this product. While the data shows that STK®-Lab is more sensitive than AP-Spot test, the STK products are more costly and require the use of a UV light

Modernizing Markov Chains Monte Carlo for Scientific and Bayesian Modeling

The advent of probabilistic programming languages has galvanized scientists to write increasingly diverse models to analyze data. Probabilistic models use a joint distribution over observed and latent variables to describe at once elaborate scientific theories, non-trivial measurement procedures, information from previous studies, and more. To effectively deploy these models in a data analysis, we need inference procedures which are reliable, flexible, and fast. In a Bayesian analysis, inference boils down to estimating the expectation values and quantiles of the unnormalized posterior distribution. This estimation problem also arises in the study of non-Bayesian probabilistic models, a prominent example being the Ising model of Statistical Physics. Markov chains Monte Carlo (MCMC) algorithms provide a general-purpose sampling method which can be used to construct sample estimators of moments and quantiles. Despite MCMC’s compelling theory and empirical success, many models continue to frustrate MCMC, as well as other inference strategies, effectively limiting our ability to use these models in a data analysis. These challenges motivate new developments in MCMC. The term “modernize” in the title refers to the deployment of methods which have revolutionized Computational Statistics and Machine Learning in the past decade, including: (i) hardware accelerators to support massive parallelization, (ii) approximate inference based on tractable densities, (iii) high-performance automatic differentiation and (iv) continuous relaxations of discrete systems. The growing availability of hardware accelerators such as GPUs has in the past years motivated a general MCMC strategy, whereby we run many chains in parallel with a short sampling phase, rather than a few chains with a long sampling phase. Unfortunately existing convergence diagnostics are not designed for the “many short chains” regime. This is notably the case of the popular R statistics which claims convergence only if the effective sample size per chain is large. We present the nested R, denoted nR, a generalization of R which does not conflate short chains and poor mixing, and offers a useful diagnostic provided we run enough chains and meet certain initialization conditions. Combined with nR the short chain regime presents us with the opportunity to identify optimal lengths for the warmup and sampling phases, as well as the optimal number of chains; tuning parameters of MCMC which are otherwise chosen using heuristics or trial-and-error. We next focus on semi-specialized algorithms for latent Gaussian models, arguably the most widely used of class of hierarchical models. It is well understood that MCMC often struggles with the geometry of the posterior distribution generated by these models. Using a Laplace approximation, we marginalize out the latent Gaussian variables and then integrate the remaining parameters with Hamiltonian Monte Carlo (HMC), a gradient-based MCMC. This approach combines MCMC and a distributional approximation, and offers a useful alternative to pure MCMC or pure approximation methods such as Variational Inference. We compare the three paradigms across a range of general linear models, which admit a sophisticated prior, i.e. a Gaussian process and a Horseshoe prior. To implement our scheme efficiently, we derive a novel automatic differentiation method called the adjoint-differentiated Laplace approximation. This differentiation algorithm propagates the minimal information needed to construct the gradient of the approximate marginal likelihood, and yields a scalable differentiation method that is orders of magnitude faster than state of the art differentiation for high-dimensional hyperparameters. We next discuss the application of our algorithm to models with an unconventional likelihood, going beyond the classical setting of general linear models. This necessitates a non-trivial generalization of the adjoint-differentiated Laplace approximation, which we implement using higher-order adjoint methods. The generalization works out to be both more general and more efficient. We apply the resulting method to an unconventional latent Gaussian model, identifying promising features and highlighting persistent challenges. The final chapter of this dissertation focuses on a specific but rich problem: the Ising model of Statistical Physics, and its generalization as the Potts and Spin Glass models. These models are challenging because they are discrete, precluding the immediate use of gradient-based algorithms, and exhibit multiple modes, notably at cold temperatures. We propose a new class of MCMC algorithms to draw samples from Potts models by augmenting the target space with a carefully constructed auxiliary Gaussian variable. In contrast to existing methods of a similar flavor, our algorithm can take advantage of the low-rank structure of the coupling matrix and scales linearly with the number of states in a Potts model. The method is applied to a broad range of coupling and temperature regimes and compared to several sampling methods, allowing us to paint a nuanced algorithmic landscape