arXiv subjects

Jukka Corander

Publications and source records attributed to Jukka Corander.

At least 19 recordsLinked to original sources

arXiv2025

Surrogate-based ABC matches generalized Bayesian inference under specific discrepancy and kernel choices

Generalized Bayesian inference (GBI) is an alternative inference framework motivated by robustness to modeling errors, where a specific loss function is used to link the model parameters with observed data, instead of the log-likelihood used in standard Bayesian inference. Approximate Bayesian Computation (ABC) refers in turn to a family of methods approximating the posterior distribution via a discrepancy function between the observed and simulated data instead of using the likelihood. In this paper we discuss the connection between ABC and GBI, when the loss function is defined as an expected discrepancy between the observed and simulated data from the model under consideration. We show that the resulting generalized posterior corresponds to an ABC-posterior when the latter is obtained under a Gaussian process -based surrogate model. We illustrate the behavior of the approximations as a function of specific discrepancy and kernel choices to provide insights of the relationships between these different approximate inference paradigms.

stat.ME↗

arXiv2023

Stratified distance space improves the efficiency of sequential samplers for approximate Bayesian computation

Approximate Bayesian computation (ABC) methods are standard tools for inferring parameters of complex models when the likelihood function is analytically intractable. A popular approach to improving the poor acceptance rate of the basic rejection sampling ABC algorithm is to use sequential Monte Carlo (ABC SMC) to produce a sequence of proposal distributions adapting towards the posterior, instead of generating values from the prior distribution of the model parameters. Proposal distribution for the subsequent iteration is typically obtained from a weighted set of samples, often called particles, of the current iteration of this sequence. Current methods for constructing these proposal distributions treat all the particles equivalently, regardless of the corresponding value generated by the sampler, which may lead to inefficiency when propagating the information across iterations of the algorithm. To improve sampler efficiency, we introduce a modified approach called stratified distance ABC SMC. Our algorithm stratifies particles based on their distance between the corresponding synthetic and observed data, and then constructs distinct proposal distributions for all the strata. Taking into account the distribution of distances across the particle space leads to substantially improved acceptance rate of the rejection sampling. We further show that efficiency can be gained by introducing a novel stopping rule for the sequential process based on the stratified posterior samples and demonstrate these advances by several examples.

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arXiv2023

Quantifying the common genetic variability of bacterial traits

The study of common heritability, or co-heritability, among multiple traits has been widely established in quantitative and molecular genetics. However, in bacteria, genome-based estimation of heritability has only been considered very recently and no methods are currently available for considering co-heritability. Here we introduce such a method and demonstrate its usefulness by multi-trait analyses of the three major human pathogens \textit{Escherichia coli}, \textit{Neisseria gonorrhoeae} and \textit{Streprococcus pneumoniae}. We anticipate that the increased availability of high-throughput genomic and phenotypic screens of bacterial populations will spawn ample future opportunities to understand the common molecular basis of different traits in bacteria.

q-bio.GN↗

arXiv2022

Inferring the heritability of bacterial traits in the era of machine learning

Quantification of heritability is a fundamental desideratum in genetics, which allows an assessment of the contribution of additive genetic variation to the variability of a trait of interest. The traditional computational approaches for assessing the heritability of a trait have been developed in the field of quantitative genetics. However, the rise of modern population genomics with large sample sizes has led to the development of several new machine learning based approaches to inferring heritability. In this paper, we systematically summarize recent advances in machine learning which can be used to infer heritability. We focus on an application of these methods to bacterial genomes, where heritability plays a key role in understanding phenotypes such as antibiotic resistance and virulence, which are particularly important due to the rising frequency of antimicrobial resistance. By designing a heritability model incorporating realistic patterns of genome-wide linkage disequilibrium for a frequently recombining bacterial pathogen, we test the performance of a wide spectrum of different inference methods, including also GCTA. In addition to the synthetic data benchmark, we present a comparison of the methods for antibiotic resistance traits for multiple bacterial pathogens. Insights from the benchmarking and real data analyses indicate a highly variable performance of the different methods and suggest that heritability inference would likely benefit from tailoring of the methods to the specific genetic architecture of the target organism.

stat.AP↗

arXiv2022

Likelihood-free Model Choice for Simulator-based Models with the Jensen--Shannon Divergence

Choice of appropriate structure and parametric dimension of a model in the light of data has a rich history in statistical research, where the first seminal approaches were developed in 1970s, such as the Akaike's and Schwarz's model scoring criteria that were inspired by information theory and embodied the rationale called Occam's razor. After those pioneering works, model choice was quickly established as its own field of research, gaining considerable attention in both computer science and statistics. However, to date, there have been limited attempts to derive scoring criteria for simulator-based models lacking a likelihood expression. Bayes factors have been considered for such models, but arguments have been put both for and against use of them and around issues related to their consistency. Here we use the asymptotic properties of Jensen--Shannon divergence (JSD) to derive a consistent model scoring criterion for the likelihood-free setting called JSD-Razor. Relationships of JSD-Razor with established scoring criteria for the likelihood-based approach are analyzed and we demonstrate the favorable properties of our criterion using both synthetic and real modeling examples.

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arXiv2022

Nonparametric likelihood-free inference with Jensen-Shannon divergence for simulator-based models with categorical output

Likelihood-free inference for simulator-based statistical models has recently attracted a surge of interest, both in the machine learning and statistics communities. The primary focus of these research fields has been to approximate the posterior distribution of model parameters, either by various types of Monte Carlo sampling algorithms or deep neural network -based surrogate models. Frequentist inference for simulator-based models has been given much less attention to date, despite that it would be particularly amenable to applications with big data where implicit asymptotic approximation of the likelihood is expected to be accurate and can leverage computationally efficient strategies. Here we derive a set of theoretical results to enable estimation, hypothesis testing and construction of confidence intervals for model parameters using asymptotic properties of the Jensen--Shannon divergence. Such asymptotic approximation offers a rapid alternative to more computation-intensive approaches and can be attractive for diverse applications of simulator-based models. 61

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arXiv2022

On predictive inference for intractable models via approximate Bayesian computation

Approximate Bayesian computation (ABC) is commonly used for parameter estimation and model comparison for intractable simulator-based models whose likelihood function cannot be evaluated. In this paper we instead investigate the feasibility of ABC as a generic approximate method for predictive inference, in particular, for computing the posterior predictive distribution of future observations or missing data of interest. We consider three complementary ABC approaches for this goal, each based on different assumptions regarding which predictive density of the intractable model can be sampled from. The case where only simulation from the joint density of the observed and future data given the model parameters can be used for inference is given particular attention and it is shown that the ideal summary statistic in this setting is minimal predictive sufficient instead of merely minimal sufficient (in the ordinary sense). An ABC prediction approach that takes advantage of a certain latent variable representation is also investigated. We additionally show how common ABC sampling algorithms can be used in the predictive settings considered. Our main results are first illustrated by using simple time-series models that facilitate analytical treatment, and later by using two common intractable dynamic models.

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arXiv2021

ABC of the Future

Approximate Bayesian computation (ABC) has advanced in two decades from a seminal idea to a practically applicable inference tool for simulator-based statistical models, which are becoming increasingly popular in many research domains. The computational feasibility of ABC for practical applications has been recently boosted by adopting techniques from machine learning to build surrogate models for the approximate likelihood or posterior and by the introduction of a general-purpose software platform with several advanced features, including automated parallelization. Here we demonstrate the strengths of the advances in ABC by going beyond the typical benchmark examples and considering real applications in astronomy, infectious disease epidemiology, personalised cancer therapy and financial prediction. We anticipate that the emerging success of ABC in producing actual added value and quantitative insights in the real world will continue to inspire a plethora of further applications across different fields of science, social science and technology.

stat.AP↗

arXiv2021

Prior knowledge elicitation: The past, present, and future

Specification of the prior distribution for a Bayesian model is a central part of the Bayesian workflow for data analysis, but it is often difficult even for statistical experts. In principle, prior elicitation transforms domain knowledge of various kinds into well-defined prior distributions, and offers a solution to the prior specification problem. In practice, however, we are still fairly far from having usable prior elicitation tools that could significantly influence the way we build probabilistic models in academia and industry. We lack elicitation methods that integrate well into the Bayesian workflow and perform elicitation efficiently in terms of costs of time and effort. We even lack a comprehensive theoretical framework for understanding different facets of the prior elicitation problem. Why are we not widely using prior elicitation? We analyse the state of the art by identifying a range of key aspects of prior knowledge elicitation, from properties of the modelling task and the nature of the priors to the form of interaction with the expert. The existing prior elicitation literature is reviewed and categorized in these terms. This allows recognizing under-studied directions in prior elicitation research, finally leading to a proposal of several new avenues to improve prior elicitation methodology.

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arXiv2021

Global and local epidemiology of Group A Streptococcus indicates that naturally-acquired immunity is enduring and strain-specific

The bacterium Group A Streptococcus (Streptococcus pyogenes, GAS) is a human-specific pathogen and a major cause of global morbidity and mortality. Despite decades of research our knowledge of GAS infection and immunity is incomplete, hampering vaccine design and other efforts to reduce disease prevalence. Epidemiological studies indicate positive associations between the prevalence of GAS-related disease, the diversity of circulating strains and the degree of poverty in host populations. However, the infection and immune mechanisms underlying these associations are not clear. In this work, we use an agent-based model to demonstrate that observed diversity and prevalence are best accounted for by the hypothesis that GAS infection confers enduring strain-specific immunity, with reduced or absent cross-protection against infection by other strains. Our results suggest that the success of GAS vaccines will depend on their ability to elicit long-lasting cross-protective immunity over multiple strain types.

q-bio.PE↗

arXiv2021

T-SNE Is Not Optimized to Reveal Clusters in Data

Cluster visualization is an essential task for nonlinear dimensionality reduction as a data analysis tool. It is often believed that Student t-Distributed Stochastic Neighbor Embedding (t-SNE) can show clusters for well clusterable data, with a smaller Kullback-Leibler divergence corresponding to a better quality. There was even theoretical proof for the guarantee of this property. However, we point out that this is not necessarily the case -- t-SNE may leave clustering patterns hidden despite strong signals present in the data. Extensive empirical evidence is provided to support our claim. First, several real-world counter-examples are presented, where t-SNE fails even if the input neighborhoods are well clusterable. Tuning hyperparameters in t-SNE or using better optimization algorithms does not help solve this issue because a better t-SNE learning objective can correspond to a worse cluster embedding. Second, we check the assumptions in the clustering guarantee of t-SNE and find they are often violated for real-world data sets.

cs.LG↗

arXiv2021

Likelihood-Free Inference with Deep Gaussian Processes

In recent years, surrogate models have been successfully used in likelihood-free inference to decrease the number of simulator evaluations. The current state-of-the-art performance for this task has been achieved by Bayesian Optimization with Gaussian Processes (GPs). While this combination works well for unimodal target distributions, it is restricting the flexibility and applicability of Bayesian Optimization for accelerating likelihood-free inference more generally. We address this problem by proposing a Deep Gaussian Process (DGP) surrogate model that can handle more irregularly behaved target distributions. Our experiments show how DGPs can outperform GPs on objective functions with multimodal distributions and maintain a comparable performance in unimodal cases. This confirms that DGPs as surrogate models can extend the applicability of Bayesian Optimization for likelihood-free inference (BOLFI), while adding computational overhead that remains negligible for computationally intensive simulators.

cs.LG↗

arXiv2021

High-dimensional structure learning of sparse vector autoregressive models using fractional marginal pseudo-likelihood

Learning vector autoregressive models from multivariate time series is conventionally approached through least squares or maximum likelihood estimation. These methods typically assume a fully connected model which provides no direct insight to the model structure and may lead to highly noisy estimates of the parameters. Because of these limitations, there has been an increasing interest towards methods that produce sparse estimates through penalized regression. However, such methods are computationally intensive and may become prohibitively time-consuming when the number of variables in the model increases. In this paper we adopt an approximate Bayesian approach to the learning problem by combining fractional marginal likelihood and pseudo-likelihood. We propose a novel method, PLVAR, that is both faster and produces more accurate estimates than the state-of-the-art methods based on penalized regression. We prove the consistency of the PLVAR estimator and demonstrate the attractive performance of the method on both simulated and real-world data.

stat.CO↗

arXiv2021

Stochastic Cluster Embedding

Neighbor Embedding (NE) aims to preserve pairwise similarities between data items and has been shown to yield an effective principle for data visualization. However, even the best existing NE methods such as Stochastic Neighbor Embedding (SNE) may leave large-scale patterns hidden, for example clusters, despite strong signals being present in the data. To address this, we propose a new cluster visualization method based on the Neighbor Embedding principle. We first present a family of Neighbor Embedding methods that generalizes SNE by using non-normalized Kullback-Leibler divergence with a scale parameter. In this family, much better cluster visualizations often appear with a parameter value different from the one corresponding to SNE. We also develop an efficient software that employs asynchronous stochastic block coordinate descent to optimize the new family of objective functions. Our experimental results demonstrate that the method consistently and substantially improves the visualization of data clusters compared with the state-of-the-art NE approaches.

cs.LG↗

arXiv2021

Approximate Bayesian inference from noisy likelihoods with Gaussian process emulated MCMC

We present a framework for approximate Bayesian inference when only a limited number of noisy log-likelihood evaluations can be obtained due to computational constraints, which is becoming increasingly common for applications of complex models. We model the log-likelihood function using a Gaussian process (GP) and the main methodological innovation is to apply this model to emulate the progression that an exact Metropolis-Hastings (MH) sampler would take if it was applicable. Informative log-likelihood evaluation locations are selected using a sequential experimental design strategy until the MH accept/reject decision is done accurately enough according to the GP model. The resulting approximate sampler is conceptually simple and sample-efficient. It is also more robust to violations of GP modelling assumptions compared with earlier, related "Bayesian optimisation-like" methods tailored for Bayesian inference. We discuss some theoretical aspects and various interpretations of the resulting approximate MH sampler, and demonstrate its benefits in the context of Bayesian and generalised Bayesian likelihood-free inference for simulator-based statistical models.

stat.ME↗

arXiv2021

Structure Learning of Contextual Markov Networks using Marginal Pseudo-likelihood

Markov networks are popular models for discrete multivariate systems where the dependence structure of the variables is specified by an undirected graph. To allow for more expressive dependence structures, several generalizations of Markov networks have been proposed. Here we consider the class of contextual Markov networks which takes into account possible context-specific independences among pairs of variables. Structure learning of contextual Markov networks is very challenging due to the extremely large number of possible structures. One of the main challenges has been to design a score, by which a structure can be assessed in terms of model fit related to complexity, without assuming chordality. Here we introduce the marginal pseudo-likelihood as an analytically tractable criterion for general contextual Markov networks. Our criterion is shown to yield a consistent structure estimator. Experiments demonstrate the favorable properties of our method in terms of predictive accuracy of the inferred models.

stat.ME↗

arXiv2020

Likelihood-free inference by ratio estimation

We consider the problem of parametric statistical inference when likelihood computations are prohibitively expensive but sampling from the model is possible. Several so-called likelihood-free methods have been developed to perform inference in the absence of a likelihood function. The popular synthetic likelihood approach infers the parameters by modelling summary statistics of the data by a Gaussian probability distribution. In another popular approach called approximate Bayesian computation, the inference is performed by identifying parameter values for which the summary statistics of the simulated data are close to those of the observed data. Synthetic likelihood is easier to use as no measure of `closeness' is required but the Gaussianity assumption is often limiting. Moreover, both approaches require judiciously chosen summary statistics. We here present an alternative inference approach that is as easy to use as synthetic likelihood but not as restricted in its assumptions, and that, in a natural way, enables automatic selection of relevant summary statistic from a large set of candidates. The basic idea is to frame the problem of estimating the posterior as a problem of estimating the ratio between the data generating distribution and the marginal distribution. This problem can be solved by logistic regression, and including regularising penalty terms enables automatic selection of the summary statistics relevant to the inference task. We illustrate the general theory on canonical examples and employ it to perform inference for challenging stochastic nonlinear dynamical systems and high-dimensional summary statistics.

stat.ML↗

arXiv2020

Generalised Bayes Updates with $f$-divergences through Probabilistic Classifiers

A stream of algorithmic advances has steadily increased the popularity of the Bayesian approach as an inference paradigm, both from the theoretical and applied perspective. Even with apparent successes in numerous application fields, a rising concern is the robustness of Bayesian inference in the presence of model misspecification, which may lead to undesirable extreme behavior of the posterior distributions for large sample sizes. Generalized belief updating with a loss function represents a central principle to making Bayesian inference more robust and less vulnerable to deviations from the assumed model. Here we consider such updates with $f$-divergences to quantify a discrepancy between the assumed statistical model and the probability distribution which generated the observed data. Since the latter is generally unknown, estimation of the divergence may be viewed as an intractable problem. We show that the divergence becomes accessible through the use of probabilistic classifiers that can leverage an estimate of the ratio of two probability distributions even when one or both of them is unknown. We demonstrate the behavior of generalized belief updates for various specific choices under the $f$-divergence family. We show that for specific divergence functions such an approach can even improve on methods evaluating the correct model likelihood function analytically.

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