Lossless, scalable implicit likelihood inference for cosmological fields

We present a comparison of simulation-based inference to full, field-based analytical inference in cosmological data analysis. To do so, we explore parameter inference for two cases where the information content is calculable analytically: Gaussian random fields whose covariance depends on parameters through the power spectrum; and correlated lognormal fields with cosmological power spectra. We compare two inference techniques: i) explicit field-level inference using the known likelihood and ii) implicit likelihood inference with maximally informative summary statistics compressed via Information Maximising Neural Networks (IMNNs). We find that a) summaries obtained from convolutional neural network compression do not lose information and therefore saturate the known field information content, both for the Gaussian covariance and the lognormal cases, b) simulation-based inference using these maximally informative nonlinear summaries recovers nearly losslessly the exact posteriors of field-level inference, bypassing the need to evaluate expensive likelihoods or invert covariance matrices, and c) even for this simple example, implicit, simulation-based likelihood incurs a much smaller computational cost than inference with an explicit likelihood. This work uses a new IMNN implementation in Jax that can take advantage of fully-differentiable simulation and inference pipeline. We also demonstrate that a single retraining of the IMNN summaries effectively achieves the theoretically maximal information, enhancing the robustness to the choice of fiducial model where the IMNN is trained.

The Influence of Model Violation on Phylogenetic Inference: A Simulation Study

Phylogenetic inference typically assumes that the data has evolved under Stationary, Reversible and Homogeneous (SRH) conditions. Many empirical and simulation studies have shown that assuming SRH conditions can lead to significant errors in phylogenetic inference when the data violates these assumptions. Yet, many simulation studies focused on extreme non-SRH conditions that represent worst-case scenarios and not the average empirical dataset. In this study, we simulate datasets under various degrees of non-SRH conditions using empirically derived parameters to mimic real data and examine the effects of incorrectly assuming SRH conditions on inferring phylogenies. Our results show that maximum likelihood inference is generally quite robust to a wide range of SRH model violations but is inaccurate under extreme convergent evolution.

Addressing cluster-constant covariates in mixed effects models via likelihood-based boosting techniques

Boosting techniques from the field of statistical learning have grown to be a popular tool for estimating and selecting predictor effects in various regression models and can roughly be separated in two general approaches, namely gradient boosting and likelihood-based boosting. An extensive framework has been proposed in order to fit generalized mixed models based on boosting, however for the case of cluster-constant covariates likelihood-based boosting approaches tend to mischoose variables in the selection step leading to wrong estimates. We propose an improved boosting algorithm for linear mixed models, where the random effects are properly weighted, disentangled from the fixed effects updating scheme and corrected for correlations with cluster-constant covariates in order to improve quality of estimates and in addition reduce the computational effort. The method outperforms current state-of-the-art approaches from boosting and maximum likelihood inference which is shown via simulations and various data examples.

Generative hypergraph clustering: From blockmodels to modularity

Hypergraphs are a natural modeling paradigm for networked systems with multiway interactions. A standard task in network analysis is the identification of closely related or densely interconnected nodes. We propose a probabilistic generative model of clustered hypergraphs with heterogeneous node degrees and edge sizes. Approximate maximum likelihood inference in this model leads to a clustering objective that generalizes the popular modularity objective for graphs. From this, we derive an inference algorithm that generalizes the Louvain graph community detection method, and a faster, specialized variant in which edges are expected to lie fully within clusters. Using synthetic and empirical data, we demonstrate that the specialized method is highly scalable and can detect clusters where graph-based methods fail. We also use our model to find interpretable higher-order structure in school contact networks, U.S. congressional bill cosponsorship and committees, product categories in copurchasing behavior, and hotel locations from web browsing sessions.

Statistical Inference for Periodic Self-Exciting Threshold Integer-Valued Autoregressive Processes

This paper considers the periodic self-exciting threshold integer-valued autoregressive processes under a weaker condition in which the second moment is finite instead of the innovation distribution being given. The basic statistical properties of the model are discussed, the quasi-likelihood inference of the parameters is investigated, and the asymptotic behaviors of the estimators are obtained. Threshold estimates based on quasi-likelihood and least squares methods are given. Simulation studies evidence that the quasi-likelihood methods perform well with realistic sample sizes and may be superior to least squares and maximum likelihood methods. The practical application of the processes is illustrated by a time series dataset concerning the monthly counts of claimants collecting short-term disability benefits from the Workers’ Compensation Board (WCB). In addition, the forecasting problem of this dataset is addressed.