The horseshoe prior is known to possess many desirable properties for Bayesian estimation of sparse parameter vectors, yet its density function lacks an analytic form. As such, it is challenging to find a closed-form solution for the posterior mode. Conventional horseshoe estimators use the posterior mean to estimate the parameters, but these estimates are not sparse. We propose a novel expectation-maximisation (EM) procedure for computing the MAP estimates of the parameters in the case of the standard linear model. A particular strength of our approach is that the M-step depends only on the form of the prior and it is independent of the form of the likelihood. We introduce several simple modifications of this EM procedure that allow for straightforward extension to generalised linear models. In experiments performed on simulated and real data, our approach performs comparable, or superior to, state-of-the-art sparse estimation methods in terms of statistical performance and computational cost.

Active learning enables efficient model training by leveraging interactions between machine learning agents and human annotators. We study and propose a novel framework that formulates batch active learning from the sparse approximation's perspective. Our active learning method aims to find an informative subset from the unlabeled data pool such that the corresponding training loss function approximates its full data pool counterpart. We realize the framework as sparsity-constrained discontinuous optimization problems, which explicitly balance uncertainty and representation for large-scale applications and could be solved by greedy or proximal iterative hard thresholding algorithms. The proposed method can adapt to various settings, including both Bayesian and non-Bayesian neural networks. Numerical experiments show that our work achieves competitive performance across different settings with lower computational complexity.

Single-cell technologies are revolutionizing the entire field of biology. The large volumes of data generated by single-cell technologies are high-dimensional, sparse, heterogeneous, and have complicated dependency structures, making analyses using conventional machine learning approaches challenging and impractical. In tackling these challenges, deep learning often demonstrates superior performance compared to traditional machine learning methods. In this work, we give a comprehensive survey on deep learning in single-cell analysis. We first introduce background on single-cell technologies and their development, as well as fundamental concepts of deep learning including the most popular deep architectures. We present an overview of the single-cell analytic pipeline pursued in research applications while noting divergences due to data sources or specific applications. We then review seven popular tasks spanning through different stages of the single-cell analysis pipeline, including multimodal integration, imputation, clustering, spatial domain identification, cell-type deconvolution, cell segmentation, and cell-type annotation. Under each task, we describe the most recent developments in classical and deep learning methods and discuss their advantages and disadvantages. Deep learning tools and benchmark datasets are also summarized for each task. Finally, we discuss the future directions and the most recent challenges. This survey will serve as a reference for biologists and computer scientists, encouraging collaborations.

Learning curves provide insight into the dependence of a learner's generalization performance on the training set size. This important tool can be used for model selection, to predict the effect of more training data, and to reduce the computational complexity of model training and hyperparameter tuning. This review recounts the origins of the term, provides a formal definition of the learning curve, and briefly covers basics such as its estimation. Our main contribution is a comprehensive overview of the literature regarding the shape of learning curves. We discuss empirical and theoretical evidence that supports well-behaved curves that often have the shape of a power law or an exponential. We consider the learning curves of Gaussian processes, the complex shapes they can display, and the factors influencing them. We draw specific attention to examples of learning curves that are ill-behaved, showing worse learning performance with more training data. To wrap up, we point out various open problems that warrant deeper empirical and theoretical investigation. All in all, our review underscores that learning curves are surprisingly diverse and no universal model can be identified.

Structural alterations have been thoroughly investigated in the brain during the early onset of schizophrenia (SCZ) with the development of neuroimaging methods. The objective of the paper is an efficient classification of SCZ in 2 different classes: Cognitive Normal (CN), and SCZ using magnetic resonance imaging (MRI) images. This paper proposed a lightweight 3D convolutional neural network (CNN) based framework for SCZ diagnosis using MRI images. In the proposed model, lightweight 3D CNN is used to extract both spatial and spectral features simultaneously from 3D volume MRI scans, and classification is done using an ensemble bagging classifier. Ensemble bagging classifier contributes to preventing overfitting, reduces variance, and improves the model's accuracy. The proposed algorithm is tested on datasets taken from three benchmark databases available as open-source: MCICShare, COBRE, and fBRINPhase-II. These datasets have undergone preprocessing steps to register all the MRI images to the standard template and reduce the artifacts. The model achieves the highest accuracy 92.22%, sensitivity 94.44%, specificity 90%, precision 90.43%, recall 94.44%, F1-score 92.39% and G-mean 92.19% as compared to the current state-of-the-art techniques. The performance metrics evidenced the use of this model to assist the clinicians for automatic accurate diagnosis of SCZ.

Existing deep-learning based tomographic image reconstruction methods do not provide accurate estimates of reconstruction uncertainty, hindering their real-world deployment. This paper develops a method, termed as the linearised deep image prior (DIP), to estimate the uncertainty associated with reconstructions produced by the DIP with total variation regularisation (TV). Specifically, we endow the DIP with conjugate Gaussian-linear model type error-bars computed from a local linearisation of the neural network around its optimised parameters. To preserve conjugacy, we approximate the TV regulariser with a Gaussian surrogate. This approach provides pixel-wise uncertainty estimates and a marginal likelihood objective for hyperparameter optimisation. We demonstrate the method on synthetic data and real-measured high-resolution 2D $\mu$CT data, and show that it provides superior calibration of uncertainty estimates relative to previous probabilistic formulations of the DIP. Our code is available at https://github.com/educating-dip/bayes_dip.

Mixture of factor analyzer (MFA) model is an efficient model for the analysis of high dimensional data through which the factor-analyzer technique based on the covariance matrices reducing the number of free parameters. The model also provides an important methodology to determine latent groups in data. There are several pieces of research to extend the model based on the asymmetrical and/or with outlier datasets with some known computational limitations that have been examined in frequentist cases. In this paper, an MFA model with a rich and flexible class of skew normal (unrestricted) generalized hyperbolic (called SUNGH) distributions along with a Bayesian structure with several computational benefits have been introduced. The SUNGH family provides considerable flexibility to model skewness in different directions as well as allowing for heavy tailed data. There are several desirable properties in the structure of the SUNGH family, including, an analytically flexible density which leads to easing up the computation applied for the estimation of parameters. Considering factor analysis models, the SUNGH family also allows for skewness and heavy tails for both the error component and factor scores. In the present study, the advantages of using this family of distributions have been discussed and the suitable efficiency of the introduced MFA model using real data examples and simulation has been demonstrated.

Standard imitation learning can fail when the expert demonstrators have different sensory inputs than the imitating agent. This is because partial observability gives rise to hidden confounders in the causal graph. We break down the space of confounded imitation learning problems and identify three settings with different data requirements in which the correct imitation policy can be identified. We then introduce an algorithm for deconfounded imitation learning, which trains an inference model jointly with a latent-conditional policy. At test time, the agent alternates between updating its belief over the latent and acting under the belief. We show in theory and practice that this algorithm converges to the correct interventional policy, solves the confounding issue, and can under certain assumptions achieve an asymptotically optimal imitation performance.

The kernel function and its hyperparameters are the central model selection choice in a Gaussian process [Rasmussen and Williams, 2006]. Typically, the hyperparameters of the kernel are chosen by maximising the marginal likelihood, an approach known as Type-II maximum likelihood (ML-II). However, ML-II does not account for hyperparameter uncertainty, and it is well-known that this can lead to severely biased estimates and an underestimation of predictive uncertainty. While there are several works which employ a fully Bayesian characterisation of GPs, relatively few propose such approaches for the sparse GPs paradigm. In this work we propose an algorithm for sparse Gaussian process regression which leverages MCMC to sample from the hyperparameter posterior within the variational inducing point framework of [Titsias, 2009]. This work is closely related to Hensman et al. [2015b], but side-steps the need to sample the inducing points, thereby significantly improving sampling efficiency in the Gaussian likelihood case. We compare this scheme against natural baselines in literature along with stochastic variational GPs (SVGPs) along with an extensive computational analysis.

Normalizing flows are constructed from a base distribution with a known density and a diffeomorphism with a tractable Jacobian. The base density of a normalizing flow can be parameterised by a different normalizing flow, thus allowing maps to be found between arbitrary distributions. We demonstrate and explore the utility of this approach and show it is particularly interesting in the case of conditional normalizing flows and for introducing optimal transport constraints on maps that are constructed using normalizing flows.