nils-herrmann/clean_scirepeval huggingface dataset:
ANALYSIS OF A NONREVERSIBLE MARKOV CHAIN SAMPLER

We analyze the convergence to stationarity of a simple nonreversible Markov chain that serves as a model for several nonreversible Markov chain sampling methods that are used in practice. Our theoretical and numerical results show that nonreversibility can indeed lead to improvements over the diffusive behavior of simple Markov chain sampling schemes. The analysis uses both probabilistic techniques and an explicit diagonalization. 1.  Markov chain sampling methods are commonly used in statistics [33, 32], computer science , statistical mechanics  and quantum field theory [34, 23]. In all these fields, distributions are encountered that are difficult to sample from directly, but for which a Markov chain that converges to the distribution can easily be constructed. For many such methods (e.g., the Metropolis algorithm , and the Gibbs sampler [17, 16] with a random scan) the Markov chain constructed is reversible. Some of these methods explore the distribution by means of a diffusive random walk. We use the term “diffusive” for processes like the ordinary random walk on a d-dimensional lattice which require time of order T 2 to travel distance T. Some other common methods, such as the Gibbs sampler with a systematic scan, use a Markov chain that is not reversible, but have diffusive behavior resembling that of a related reversible chain [30]. Some Markov chain methods attempt to avoid the inefficiencies of such diffusive exploration. The Hybrid Monte Carlo method  uses an elaborate Metropolis proposal that can make large changes to the state. In a variant of this method due to Horowitz [21], a similar effect is produced using a Markov chain that is carefully designed to be nonreversible.  for reviews of these methods.) The overrelaxation method  also employs a nonreversible Markov chain as a way of suppressing diffusive behavior, as discussed in [29]. In this paper, we analyze a nonreversible Markov chain that does a onedimensional walk, as an abstraction of these practical sampling methods, particularly that of Horowitz [21]. Gustafson  has also recently tried using adaptations of Horowitz’s method. We find that the nonreversible walk does indeed converge more rapidly than the usual simple random walk. We ana
Suppressing Random Walks in Markov Chain Monte Carlo Using Ordered Overrelaxation

Markov chain Monte Carlo methods such as Gibbs sampling and simple forms of the Metropolis algorithm typically move about the distribution being sampled via a random walk. For the complex, high-dimensional distributions commonly encountered in Bayesian inference and statistical physics, the distance moved in each iteration of these algorithms will usually be small, because it is difficult or impossible to transform the problem to eliminate dependencies between variables. The inefficiency inherent in taking such small steps is greatly exacerbated when the algorithm operates via a random walk, as in such a case moving to a point n steps away will typically take around n 2 iterations. Such random walks can sometimes be suppressed using “overrelaxed” variants of Gibbs sampling (a.k.a. the heatbath algorithm), but such methods have hitherto been largely restricted to problems where all the full conditional distributions are Gaussian. I present an overrelaxed Markov chain Monte Carlo algorithm based on order statistics that is more widely applicable. In particular, the algorithm can be applied whenever the full conditional distributions are such that their cumulative distribution functions and inverse cumulative distribution functions can be efficiently computed. The method is demonstrated on an inference problem for a simple hierarchical Bayesian model.
Arithmetic coding revisited

Over the last decade, arithmetic coding has emerged as an important compression tool. It is now the method of choice for adaptive coding on myltisymbol alphabets because of its speed, low storage requirements, and effectiveness of compression. This article describes a new implementation of arithmetic coding that incorporates several improvements over a widely used earlier version by Witten, Neal, and Cleary, which has become a de facto standard. These improvements include fewer multiplicative operations, greatly extended range of alphabet sizes and symbol probabilities, and the use of low-precision arithmetic, permitting implementation by fast shift/add operations. We also describe a modular structure that separates the coding, modeling, and probability estimation components of a compression system. To motivate the improved coder, we consider the needs of a word-based text compression program. We report a range of experimental results using this and other models. Complete source code is available.
Assessing Relevance determination methods using DELVE

Empirically assessing the predictive performance of learning methods is an essential component of research in machine learning. The DELVE environment was developed to support such assessments. It provides a collection of datasets, a standard approach to conducting experiments with these datasets, and software for the statistical analysis of experimental results. In this chapter, DELVE is used to assess the performance of neural network methods when the inputs available to the network have varying degrees of relevance. The results confirm that the Bayesian method of Automatic Relevance Determination (ARD) is often (but not always) helpful, and show that a variation on early stopping inspired by ARD is also beneficial. The experiments also reveal some other interesting characteristics of the methods tested. This example illustrates the essential role of empirical testing, and shows the strengths and weaknesses of the DELVE environment.
Markov Chain Monte Carlo in Practice: A Roundtable Discussion

Markov chain Monte Carlo (MCMC) methods make possible the use of flexible Bayesian models that would otherwise be computationally infeasible. In recent years, a great variety of such applications have been described in the literature. Applied statisticians who are new to these methods may have several questions and concerns, however: How much effort and expertise are needed to design and use a Markov chain sampler? How much confidence can one have in the answers that MCMC produces? How does the use of MCMC affect the rest of the model-building process? At the Joint Statistical Meetings in August, 1996, a panel of experienced MCMC users discussed these and other issues, as well as various “tricks of the trade” This article is an edited recreation of that discussion. Its purpose is to offer advice and guidance to novice users of MCMC—and to not-so-novice users as well. Topics include building confidence in simulation results, methods for speeding and assessing convergence, estimating standard error...
Factor Analysis Using Delta-Rule Wake-Sleep Learning

We describe a linear network that models correlations between real-valued visible variables using one or more real-valued hidden variablesa factor analysis model. This model can be seen as a linear version of the Helmholtz machine, and its parameters can be learned using the wake sleep method, in which learning of the primary generative model is as sisted by a recognition model, whose role is to fill in the values of hidden variables based on the values of visible variables. The generative and recognition models are jointly learned in wake and sleep phases, using just the delta rule. This learning procedure is comparable in simplicity to Hebbian learning, which produces a somewhat different representation of correlations in terms of principal components. We argue that the simplicity of wake-sleep learning makes factor analysis a plausible alternative to Hebbian learning as a model of activity-dependent cortical plasticity.
Markov Chain Monte Carlo Methods Based on `Slicing' the Density Function

One way to sample from a distribution is to sample uniformly from the region under the plot of its density function. A Markov chain that converges to this uniform distribution can be constructed by alternating uniform sampling in the vertical direction with uniform sampling from the horizontaìslice' deened by the current vertical position. Variations on such`slice sampling' methods can easily be implemented for univariate distributions , and can be used to sample from a multivariate distribution by updating each variable in turn. This approach is often easier to implement than Gibbs sampling, and may be more eecient than easily-constructed versions of the Metropolis algorithm. Slice sampling is therefore attractive in routine Markov chain Monte Carlo applications, and for use by software that automatically generates a Markov chain sampler from a model specii-cation. One can also easily devise overrelaxed versions of slice sampling, which sometimes greatly improve sampling eeciency by suppressing random walk behaviour. Random walks can also be avoided in some slice sampling schemes that simultaneously update all variables.
Monte Carlo Implementation of Gaussian Process Models for Bayesian Regression and Classification

Gaussian processes are a natural way of defining prior distributions over functions of one or more input variables. In a simple nonparametric regression problem, where such a function gives the mean of a Gaussian distribution for an observed response, a Gaussian process model can easily be implemented using matrix computations that are feasible for datasets of up to about a thousand cases. Hyperparameters that define the covariance function of the Gaussian process can be sampled using Markov chain methods. Regression models where the noise has a t distribution and logistic or probit models for classification applications can be implemented by sampling as well for latent values underlying the observations. Software is now available that implements these methods using covariance functions with hierarchical parameterizations. Models defined in this way can discover high-level properties of the data, such as which inputs are relevant to predicting the response.
Priors for Infinite Networks

In this chapter, I show that priors over network parameters can be defined in such a way that the corresponding priors over functions computed by the network reach reasonable limits as the number of hidden units goes to infinity. When using such priors,there is thus no need to limit the size of the network in order to avoid “overfitting”. The infinite network limit also provides insight into the properties of different priors. A Gaussian prior for hidden-to-output weights results in a Gaussian process prior for functions,which may be smooth, Brownian, or fractional Brownian. Quite different effects can be obtained using priors based on non-Gaussian stable distributions. In networks with more than one hidden layer, a combination of Gaussian and non-Gaussian priors appears most interesting.
Sampling from multimodal distributions using tempered transitions

I present a new Markov chain sampling method appropriate for distributions with isolated modes. Like the recently developed method of ‘simulated tempering’, the ‘tempered transition’ method uses a series of distributions that interpolate between the distribution of interest and a distribution for which sampling is easier. The new method has the advantage that it does not require approximate values for the normalizing constants of these distributions, which are needed for simulated tempering, and can be tedious to estimate. Simulated tempering performs a random walk along the series of distributions used. In contrast, the tempered transitions of the new method move systematically from the desired distribution, to the easily-sampled distribution, and back to the desired distribution. This systematic movement avoids the inefficiency of a random walk, an advantage that is unfortunately cancelled by an increase in the number of interpolating distributions required. Because of this, the sampling efficiency of the tempered transition method in simple problems is similar to that of simulated tempering. On more complex distributions, however, simulated tempering and tempered transitions may perform differently. Which is better depends on the ways in which the interpolating distributions are ‘deceptive’.
Evaluation of Neural Network Models

This chapter reports empirical evaluations of the predictive performance of Bayesian neural network models applied to several synthetic and real data sets. Good results were obtained when large networks with appropriate priors were used on small data sets for a synthetic regression problem, confirming expectations based on properties of the associated priors over functions. The Automatic Relevance Determination model was effective in suppressing irrelevant inputs in tests on synthetic regression and classification problems. Tests on two real data sets showed that Bayesian neural network models, implemented using hybrid Monte Carlo, can produce good results when applied to realistic problems of moderate size.
Monte Carlo Implementation

This chapter presents a Markov chain Monte Carlo implementation of Bayesian learning for neural networks in which network parameters are updated using the hybrid Monte Carlo algorithm, a form of the Metropolis algorithm in which candidate states are found by means of dynamical simulation. Hyperparameters are updated separately using Gibbs sampling, allowing their values to be used in chosing good stepsizes for the discretized dynamics. I show that hybrid Monte Carlo performs better than simple Metropolis,due to its avoidance of random walk behaviour. I also discuss variants of hybrid Monte Carlo in which dynamical computations are done using “partial gradients”, in which acceptance is based on a “window” of states,and in which momentum updates incorporate “persistence”.
Conclusions and Further Work

The preceding three chapters have examined the meaning of Bayesian neural network models, showed how these models can be implemented by Markov chain Monte Carlo methods, and demonstrated that such an implementation can be applied in practice to problems of moderate size, with good results. In this concluding chapter, I will review what has been accomplished in these areas, and describe on-going and potential future work to extend these results, both for neural networks and for other flexible Bayesian models.
Arithmetic coding revisited

During its long gestation in the 1970s and early 1980s, arithmetic coding was widely regarded more as an academic curiosity than a practical coding technique. One factor that helped it gain the popularity it enjoys today was the publication in 1987 of source code for a multi symbol arithmetic coder in Communications of the ACM. Now (1995), our understanding of arithmetic coding has further matured, and it is timely to review the components of that implementation and summarise the improvements that we and other authors have developed since then. We also describe a novel method for performing the underlying calculation needed for arithmetic coding. Accompanying the paper is a "Mark II" implementation that incorporates the improvements we suggest. The areas examined include: changes to the coding procedure that reduce the number of multiplications and divisions and permit them to be done to low precision; the increased range of probability approximations and alphabet sizes that can be supported using limited precision calculation; data structures for support of arithmetic coding on large alphabets; the interface between the modelling and coding subsystems; the use of enhanced models to allow high performance compression. For each of these areas, we consider how the new implementation differs from the CACM package.
Bayesian Learning for Neural Networks

Artificial "neural networks" are widely used as flexible models for classification and regression applications, but questions remain about how the power of these models can be safely exploited when training data is limited. This book demonstrates how Bayesian methods allow complex neural network models to be used without fear of the "overfitting" that can occur with traditional training methods. Insight into the nature of these complex Bayesian models is provided by a theoretical investigation of the priors over functions that underlie them. A practical implementation of Bayesian neural network learning using Markov chain Monte Carlo methods is also described, and software for it is freely available over the Internet. Presupposing only basic knowledge of probability and statistics, this book should be of interest to researchers in statistics, engineering, and artificial intelligence.
Max – Planck – Institut f ür biologische Kybernetik Max Planck Institute for Biological Cybernetics Technical Report No . 136 Approximate Inference for Robust Gaussian Process Regression

Gaussian process (GP) priors have been successfully used in non-parametric Bayesian regression and classification models. Inference can be performed analytically only for the regression model with Gaussian noise. For all other likelihood models inference is intractable and various approximation techniques have been proposed. In recent years xpectation-propagation(EP) has been developed as a general method for approximate inference. This article provides a general summary of how expectationpropagation can be used for approximate inference in Gaussian process models. Furthermore we present a case study describing its implementation for a new robust variant of Gaussian process regression. To gain further insights into the quality of the EP approximation we present experiments in which we compare to results obtained by Markov chain Monte Carlo(MCMC) sampling.
Evaluating Predictive Uncertainty Challenge

This Chapter presents the PASCAL Evaluating Predictive Uncertainty Challenge, introduces the contributed Chapters by the participants who obtained outstanding results, and provides a discussion with some lessons to be learnt. The Challenge was set up to evaluate the ability of Machine Learning algorithms to provide good “probabilistic predictions”, rather than just the usual “point predictions” with no measure of uncertainty, in regression and classification problems. Parti-cipants had to compete on a number of regression and classification tasks, and were evaluated by both traditional losses that only take into account point predictions and losses we proposed that evaluate the quality of the probabilistic predictions.
Assessing Approximate Inference for Binary Gaussian Process Classification

Gaussian process priors can be used to define flexible, probabilistic classification models. Unfortunately exact Bayesian inference is analytically intractable and various approximation techniques have been proposed. In this work we review and compare Laplace's method and Expectation Propagation for approximate Bayesian inference in the binary Gaussian process classification model. We present a comprehensive comparison of the approximations, their predictive performance and marginal likelihood estimates to results obtained by MCMC sampling. We explain theoretically and corroborate empirically the advantages of Expectation Propagation compared to Laplace's method.
A Unifying View of Sparse Approximate Gaussian Process Regression

We provide a new unifying view, including all existing proper probabilistic sparse approximations for Gaussian process regression. Our approach relies on expressing the effective prior which the methods are using. This allows new insights to be gained, and highlights the relationship between existing methods. It also allows for a clear theoretically justified ranking of the closeness of the known approximations to the corresponding full GPs. Finally we point directly to designs of new better sparse approximations, combining the best of the existing strategies, within attractive computational constraints.
Approximate inference for robust Gaussian process regression

Gaussian process (GP) priors have been successfully used in non-parametric Bayesian regression and classification models. Inference can be performed analytically only for the regression model with Gaussian noise. For all other likelihood models inference is intractable and various approximation techniques have been proposed. In recent years expectation-propagation (EP) has been developed as a general method for approximate inference. This article provides a general summary of how expectationpropagation can be used for approximate inference in Gaussian process models. Furthermore we present a case study describing its implementation for a new robust variant of Gaussian process regression. To gain further insights into the quality of the EP approximation we present experiments in which we compare to results obtained by Markov chain Monte Carlo (MCMC) sampling.
Healing the relevance vector machine through augmentation

The Relevance Vector Machine (RVM) is a sparse approximate Bayesian kernel method. It provides full predictive distributions for test cases. However, the predictive uncertainties have the unintuitive property, that they get smaller the further you move away from the training cases. We give a thorough analysis. Inspired by the analogy to non-degenerate Gaussian Processes, we suggest augmentation to solve the problem. The purpose of the resulting model, RVM*, is primarily to corroborate the theoretical and experimental analysis. Although RVM* could be used in practical applications, it is no longer a truly sparse model. Experiments show that sparsity comes at the expense of worse predictive. distributions.
Modelling Spikes with Mixtures of Factor Analysers

Identifying the action potentials of individual neurons from extracellular recordings, known as spike sorting, is a challenging problem. We consider the spike sorting problem using a generative model, mixtures of factor analysers, which concurrently performs clustering and feature extraction. The most important advantage of this method is that it quantifies the certainty with which the spikes are classified. This can be used as a means for evaluating the quality of clustering and therefore spike isolation. Using this method, nearly simultaneously occurring spikes can also be modelled which is a hard task for many of the spike sorting methods. Furthermore, modelling the data with a generative model allows us to generate simulated data.
Gaussian process model based predictive control

Gaussian process models provide a probabilistic non-parametric modelling approach for black-box identification of non-linear dynamic systems. The Gaussian processes can highlight areas of the input space where prediction quality is poor, due to the lack of data or its complexity, by indicating the higher variance around the predicted mean. Gaussian process models contain noticeably less coefficients to be optimized. This paper illustrates possible application of Gaussian process models within model-based predictive control. The extra information provided within Gaussian process model is used in predictive control, where optimization of control signal takes the variance information into account. The predictive control principle is demonstrated on control of pH process benchmark.
Learning Depth from Stereo

We compare two approaches to the problem of estimating the depth of a point in space from observing its image position in two different cameras: 1. The classical photogrammetric approach explicitly models the two cameras and estimates their intrinsic and extrinsic parameters using a tedious calibration procedure; 2. A generic machine learning approach where the mapping from image to spatial coordinates is directly approximated by a Gaussian Process regression. Our results show that the generic learning approach, in addition to simplifying the procedure of calibration, can lead to higher depth accuracies than classical calibration although no specific domain knowledge is used.