Variational autoencoders (VAEs) often suffer from posterior collapse, which is a phenomenon in which the learned latent space becomes uninformative. This is often related to the hyperparameter resembling the data variance. It can be shown that an inappropriate choice of this hyperparameter causes the oversmoothness in the linearly approximated case and can be empirically verified for the general cases. Moreover, determining such appropriate choice becomes infeasible if the data variance is non-uniform or conditional. Therefore, we propose VAE extensions with generalized parameterizations of the data variance and incorporate maximum likelihood estimation into the objective function to adaptively regularize the decoder smoothness. The images generated from proposed VAE extensions show improved Fr\'echet inception distance (FID) on MNIST and CelebA datasets.

Sight and hearing are two senses that play a vital role in human communication and scene understanding. To mimic human perception ability, audio-visual learning, aimed at developing computational approaches to learn from both audio and visual modalities, has been a flourishing field in recent years. A comprehensive survey that can systematically organize and analyze studies of the audio-visual field is expected. Starting from the analysis of audio-visual cognition foundations, we introduce several key findings that have inspired our computational studies. Then, we systematically review the recent audio-visual learning studies and divide them into three categories: audio-visual boosting, cross-modal perception and audio-visual collaboration. Through our analysis, we discover that, the consistency of audio-visual data across semantic, spatial and temporal support the above studies. To revisit the current development of the audio-visual learning field from a more macro view, we further propose a new perspective on audio-visual scene understanding, then discuss and analyze the feasible future direction of the audio-visual learning area. Overall, this survey reviews and outlooks the current audio-visual learning field from different aspects. We hope it can provide researchers with a better understanding of this area. A website including constantly-updated survey is released: \url{https://gewu-lab.github.io/audio-visual-learning/}.

Variational Bayes (VB) applied to latent Dirichlet allocation (LDA) has become the most popular algorithm for aspect modeling. While sufficiently successful in text topic extraction from large corpora, VB is less successful in identifying aspects in the presence of limited data. We present a novel variational message passing algorithm as applied to Latent Dirichlet Allocation (LDA) and compare it with the gold standard VB and collapsed Gibbs sampling. In situations where marginalisation leads to non-conjugate messages, we use ideas from sampling to derive approximate update equations. In cases where conjugacy holds, Loopy Belief update (LBU) (also known as Lauritzen-Spiegelhalter) is used. Our algorithm, ALBU (approximate LBU), has strong similarities with Variational Message Passing (VMP) (which is the message passing variant of VB). To compare the performance of the algorithms in the presence of limited data, we use data sets consisting of tweets and news groups. Using coherence measures we show that ALBU learns latent distributions more accurately than does VB, especially for smaller data sets.

Of late, in order to have better acceptability among various domain, researchers have argued that machine intelligence algorithms must be able to provide explanations that humans can understand causally. This aspect, also known as'causability' achieves a specific level of human-level explainability. A specific class of algorithms known as counterfactuals may be able to provide causability. In statistics, causality has been studied and applied for many years, but not in great detail in artificial intelligence (AI). In a first-of-its-kind study, we employed the principles of causal inference to provide explainability for solving the analytical customer relationship management (ACRM) problems. In the context of banking and insurance, current research on interpretability tries to address causality-related questions like why did this model make such decisions, and was the model's choice influenced by a particular factor? We propose a solution in the form of an intervention, wherein the effect of changing the distribution of features of ACRM datasets is studied on the target feature. Subsequently, a set of counterfactuals is also obtained that may be furnished to any customer who demands an explanation of the decision taken by the bank/insurance company. Except for the credit card churn prediction dataset, good quality counterfactuals were generated for the loan default, insurance fraud detection, and credit card fraud detection datasets, where changes in no more than three features are observed.

Recent progress in machine learning methods, and the emerging availability of programmable interfaces for scanning probe microscopes (SPMs), have propelled automated and autonomous microscopies to the forefront of attention of the scientific community. However, enabling automated microscopy requires the development of task-specific machine learning methods, understanding the interplay between physics discovery and machine learning, and fully defined discovery workflows. This, in turn, requires balancing the physical intuition and prior knowledge of the domain scientist with rewards that define experimental goals and machine learning algorithms that can translate these to specific experimental protocols. Here, we discuss the basic principles of Bayesian active learning and illustrate its applications for SPM. We progress from the Gaussian Process as a simple data-driven method and Bayesian inference for physical models as an extension of physics-based functional fits to more complex deep kernel learning methods, structured Gaussian Processes, and hypothesis learning. These frameworks allow for the use of prior data, the discovery of specific functionalities as encoded in spectral data, and exploration of physical laws manifesting during the experiment. The discussed framework can be universally applied to all techniques combining imaging and spectroscopy, SPM methods, nanoindentation, electron microscopy and spectroscopy, and chemical imaging methods, and can be particularly impactful for destructive or irreversible measurements.

Normalizing Flows (NFs) are flexible explicit generative models that have been shown to accurately model complex real-world data distributions. However, their invertibility constraint imposes limitations on data distributions that reside on lower dimensional manifolds embedded in higher dimensional space. Practically, this shortcoming is often bypassed by adding noise to the data which impacts the quality of the generated samples. In contrast to prior work, we approach this problem by generating samples from the original data distribution given full knowledge about the perturbed distribution and the noise model. To this end, we establish that NFs trained on perturbed data implicitly represent the manifold in regions of maximum likelihood. Then, we propose an optimization objective that recovers the most likely point on the manifold given a sample from the perturbed distribution. Finally, we focus on 3D point clouds for which we utilize the explicit nature of NFs, i.e. surface normals extracted from the gradient of the log-likelihood and the log-likelihood itself, to apply Poisson surface reconstruction to refine generated point sets.

Sharing medical data between institutions is difficult in practice due to data protection laws and official procedures within institutions. Therefore, most existing algorithms are trained on relatively small electroencephalogram (EEG) data sets which is likely to be detrimental to prediction accuracy. In this work, we simulate a case when the data can not be shared by splitting the publicly available data set into disjoint sets representing data in individual institutions. We propose to train a (local) detector in each institution and aggregate their individual predictions into one final prediction. Four aggregation schemes are compared, namely, the majority vote, the mean, the weighted mean and the Dawid-Skene method. The method was validated on an independent data set using only a subset of EEG channels. The ensemble reaches accuracy comparable to a single detector trained on all the data when sufficient amount of data is available in each institution. The weighted mean aggregation scheme showed best performance, it was only marginally outperformed by the Dawid--Skene method when local detectors approach performance of a single detector trained on all available data.

We show that deep belief networks with binary hidden units can approximate any multivariate probability density under very mild integrability requirements on the parental density of the visible nodes. The approximation is measured in the $L^q$-norm for $q\in[1,\infty]$ ($q=\infty$ corresponding to the supremum norm) and in Kullback-Leibler divergence. Furthermore, we establish sharp quantitative bounds on the approximation error in terms of the number of hidden units.

We introduce a scheme for probabilistic hypocenter inversion with Stein variational inference. Our approach uses a differentiable forward model in the form of a physics informed neural network, which we train to solve the Eikonal equation. This allows for rapid approximation of the posterior by iteratively optimizing a collection of particles against a kernelized Stein discrepancy. We show that the method is well-equipped to handle highly multimodal posterior distributions, which are common in hypocentral inverse problems. A suite of experiments is performed to examine the influence of the various hyperparameters. Once trained, the method is valid for any seismic network geometry within the study area without the need to build travel time tables. We show that the computational demands scale efficiently with the number of differential times, making it ideal for large-N sensing technologies like Distributed Acoustic Sensing. The techniques outlined in this manuscript have considerable implications beyond just ray-tracing procedures, with the work flow applicable to other fields with computationally expensive inversion procedures such as full waveform inversion.

Bonus-Malus Systems (BMSs) are nowadays widely employed in automobile insurance to dynamically adjust a premium based on a customer's claims experience. The intuition behind these posterior ratemaking systems is that as we observe more claiming behavior, we learn more about the underlying risk profile. These systems are therefore a commercially attractive form of experience rating, in which we correct the prior premium for past claims to reflect our updated beliefs about a customer's risk profile. Moreover, they traditionally consider a customer's number of claims irrespective of their sizes and thus implicitly assume independence between the claim counts and sizes (Hey, 1970; Denuit et al., 2007; Boucher and Inoussa, 2014; Verschuren, 2021). Alternative Bayesian forms of experience rating typically depend only on the frequency component as well or consider the two components separately (see, e.g., Denuit and Lang (2004); Bühlmann and Gisler (2005); Mahmoudvand and Hassani (2009); Bermúdez and Karlis (2011, 2017)).