Discrete data are abundant and often arise as counts or rounded data. Yet even for linear regression models, conjugate priors and closed-form posteriors are typically unavailable, which necessitates approximations such as MCMC for posterior inference. For a broad class of count and rounded data regression models, we introduce conjugate priors that enable closed-form posterior inference. Key posterior and predictive functionals are computable analytically or via direct Monte Carlo simulation. Crucially, the predictive distributions are discrete to match the support of the data and can be evaluated or simulated jointly across multiple covariate values. These tools are broadly useful for linear regression, nonlinear models via basis expansions, and model and variable selection. Multiple simulation studies demonstrate significant advantages in computing, predictive modeling, and selection relative to existing alternatives.
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Probabilistic counters are well known tools often used for space-efficient set cardinality estimation. In this paper we investigate probabilistic counters from the perspective of preserving privacy. We use standard, rigid differential privacy notion. The intuition is that the probabilistic counters do not reveal too much information about individuals, but provide only general information about the population. Thus they can be used safely without violating privacy of individuals. It turned out however that providing a precise, formal analysis of privacy parameters of probabilistic counters is surprisingly difficult and needs advanced techniques and a very careful approach. We demonstrate also that probabilistic counters can be used as a privacy protecion mechanism without any extra randomization. That is, the inherit randomization from the protocol is sufficient for protecting privacy, even if the probabilistic counter is used many times. In particular we present a specific privacy-preserving data aggregation protocol based on a probabilistic counter. Our results can be used for example in performing distributed surveys.
I propose kernel ridge regression estimators for long term causal inference, where a short term experimental data set containing randomized treatment and short term surrogates is fused with a long term observational data set containing short term surrogates and long term outcomes. I propose estimators of treatment effects, dose responses, and counterfactual distributions with closed form solutions in terms of kernel matrix operations. I allow covariates, treatment, and surrogates to be discrete or continuous, and low, high, or infinite dimensional. For long term treatment effects, I prove $\sqrt{n}$ consistency, Gaussian approximation, and semiparametric efficiency. For long term dose responses, I prove uniform consistency with finite sample rates. For long term counterfactual distributions, I prove convergence in distribution.
Feature regression is a simple way to distill large neural network models to smaller ones. We show that with simple changes to the network architecture, regression can outperform more complex state-of-the-art approaches for knowledge distillation from self-supervised models. Surprisingly, the addition of a multi-layer perceptron head to the CNN backbone is beneficial even if used only during distillation and discarded in the downstream task. Deeper non-linear projections can thus be used to accurately mimic the teacher without changing inference architecture and time. Moreover, we utilize independent projection heads to simultaneously distill multiple teacher networks. We also find that using the same weakly augmented image as input for both teacher and student networks aids distillation. Experiments on ImageNet dataset demonstrate the efficacy of the proposed changes in various self-supervised distillation settings.
Many statistical machine approaches could ultimately highlight novel features of the etiology of complex diseases by analyzing multi-omics data. However, they are sensitive to some deviations in distribution when the observed samples are potentially contaminated with adversarial corrupted outliers (e.g., a fictional data distribution). Likewise, statistical advances lag in supporting comprehensive data-driven analyses of complex multi-omics data integration. We propose a novel non-linear M-estimator-based approach, "robust kernel machine regression (RobKMR)," to improve the robustness of statistical machine regression and the diversity of fictional data to examine the higher-order composite effect of multi-omics datasets. We address a robust kernel-centered Gram matrix to estimate the model parameters accurately. We also propose a robust score test to assess the marginal and joint Hadamard product of features from multi-omics data. We apply our proposed approach to a multi-omics dataset of osteoporosis (OP) from Caucasian females. Experiments demonstrate that the proposed approach effectively identifies the inter-related risk factors of OP. With solid evidence (p-value = 0.00001), biological validations, network-based analysis, causal inference, and drug repurposing, the selected three triplets ((DKK1, SMTN, DRGX), (MTND5, FASTKD2, CSMD3), (MTND5, COG3, CSMD3)) are significant biomarkers and directly relate to BMD. Overall, the top three selected genes (DKK1, MTND5, FASTKD2) and one gene (SIDT1 at p-value= 0.001) significantly bond with four drugs- Tacrolimus, Ibandronate, Alendronate, and Bazedoxifene out of 30 candidates for drug repurposing in OP. Further, the proposed approach can be applied to any disease model where multi-omics datasets are available.
Unobserved confounding is one of the main challenges when estimating causal effects. We propose a causal reduction method that, given a causal model, replaces an arbitrary number of possibly high-dimensional latent confounders with a single latent confounder that takes values in the same space as the treatment variable, without changing the observational and interventional distributions the causal model entails. This allows us to estimate the causal effect in a principled way from combined data without relying on the common but often unrealistic assumption that all confounders have been observed. We apply our causal reduction in three different settings. In the first setting, we assume the treatment and outcome to be discrete. The causal reduction then implies bounds between the observational and interventional distributions that can be exploited for estimation purposes. In certain cases with highly unbalanced observational samples, the accuracy of the causal effect estimate can be improved by incorporating observational data. Second, for continuous variables and assuming a linear-Gaussian model, we derive equality constraints for the parameters of the observational and interventional distributions. Third, for the general continuous setting (possibly nonlinear or non-Gaussian), we parameterize the reduced causal model using normalizing flows, a flexible class of easily invertible nonlinear transformations. We perform a series of experiments on synthetic data and find that in several cases the number of interventional samples can be reduced when adding observational training samples without sacrificing accuracy.
Opioid misuse is a national epidemic and a significant drug related threat to the United States. While the scale of the problem is undeniable, estimates of the local prevalence of opioid misuse are lacking, despite their importance to policy-making and resource allocation. This is due, in part, to the challenge of directly measuring opioid misuse at a local level. In this paper, we develop a Bayesian hierarchical spatio-temporal abundance model that integrates indirect county-level data on opioid-related outcomes with state-level survey estimates on prevalence of opioid misuse to estimate the latent county-level prevalence and counts of people who misuse opioids. A simulation study shows that our integrated model accurately recovers the latent counts and prevalence. We apply our model to county-level surveillance data on opioid overdose deaths and treatment admissions from the state of Ohio. Our proposed framework can be applied to other applications of small area estimation for hard to reach populations, which is a common occurrence with many health conditions such as those related to illicit behaviors.
The Bayesian paradigm has the potential to solve core issues of deep neural networks such as poor calibration and data inefficiency. Alas, scaling Bayesian inference to large weight spaces often requires restrictive approximations. In this work, we show that it suffices to perform inference over a small subset of model weights in order to obtain accurate predictive posteriors. The other weights are kept as point estimates. This subnetwork inference framework enables us to use expressive, otherwise intractable, posterior approximations over such subsets. In particular, we implement subnetwork linearized Laplace: We first obtain a MAP estimate of all weights and then infer a full-covariance Gaussian posterior over a subnetwork. We propose a subnetwork selection strategy that aims to maximally preserve the model's predictive uncertainty. Empirically, our approach is effective compared to ensembles and less expressive posterior approximations over full networks.
We propose a geometric convexity shape prior preservation method for variational level set based image segmentation methods. Our method is built upon the fact that the level set of a convex signed distanced function must be convex. This property enables us to transfer a complicated geometrical convexity prior into a simple inequality constraint on the function. An active set based Gauss-Seidel iteration is used to handle this constrained minimization problem to get an efficient algorithm. We apply our method to region and edge based level set segmentation models including Chan-Vese (CV) model with guarantee that the segmented region will be convex. Experimental results show the effectiveness and quality of the proposed model and algorithm.
Discrete random structures are important tools in Bayesian nonparametrics and the resulting models have proven effective in density estimation, clustering, topic modeling and prediction, among others. In this paper, we consider nested processes and study the dependence structures they induce. Dependence ranges between homogeneity, corresponding to full exchangeability, and maximum heterogeneity, corresponding to (unconditional) independence across samples. The popular nested Dirichlet process is shown to degenerate to the fully exchangeable case when there are ties across samples at the observed or latent level. To overcome this drawback, inherent to nesting general discrete random measures, we introduce a novel class of latent nested processes. These are obtained by adding common and group-specific completely random measures and, then, normalising to yield dependent random probability measures. We provide results on the partition distributions induced by latent nested processes, and develop an Markov Chain Monte Carlo sampler for Bayesian inferences. A test for distributional homogeneity across groups is obtained as a by product. The results and their inferential implications are showcased on synthetic and real data.
In this paper we introduce a covariance framework for the analysis of EEG and MEG data that takes into account observed temporal stationarity on small time scales and trial-to-trial variations. We formulate a model for the covariance matrix, which is a Kronecker product of three components that correspond to space, time and epochs/trials, and consider maximum likelihood estimation of the unknown parameter values. An iterative algorithm that finds approximations of the maximum likelihood estimates is proposed. We perform a simulation study to assess the performance of the estimator and investigate the influence of different assumptions about the covariance factors on the estimated covariance matrix and on its components. Apart from that, we illustrate our method on real EEG and MEG data sets. The proposed covariance model is applicable in a variety of cases where spontaneous EEG or MEG acts as source of noise and realistic noise covariance estimates are needed for accurate dipole localization, such as in evoked activity studies, or where the properties of spontaneous EEG or MEG are themselves the topic of interest, such as in combined EEG/fMRI experiments in which the correlation between EEG and fMRI signals is investigated.
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