Manifold learning flows are a class of generative modelling techniques that assume a low-dimensional manifold description of the data. The embedding of such a manifold into the high-dimensional space of the data is achieved via learnable invertible transformations. Therefore, once the manifold is properly aligned via a reconstruction loss, the probability density is tractable on the manifold and maximum likelihood can be used to optimize the network parameters. Naturally, the lower-dimensional representation of the data requires an injective-mapping. Recent approaches were able to enforce that the density aligns with the modelled manifold, while efficiently calculating the density volume-change term when embedding to the higher-dimensional space. However, unless the injective-mapping is analytically predefined, the learned manifold is not necessarily an efficient representation of the data. Namely, the latent dimensions of such models frequently learn an entangled intrinsic basis, with degenerate information being stored in each dimension. Alternatively, if a locally orthogonal and/or sparse basis is to be learned, here coined canonical intrinsic basis, it can serve in learning a more compact latent space representation. Toward this end, we propose a canonical manifold learning flow method, where a novel optimization objective enforces the transformation matrix to have few prominent and non-degenerate basis functions. We demonstrate that by minimizing the off-diagonal manifold metric elements $\ell_1$-norm, we can achieve such a basis, which is simultaneously sparse and/or orthogonal. Canonical manifold flow yields a more efficient use of the latent space, automatically generating fewer prominent and distinct dimensions to represent data, and a better approximation of target distributions than other manifold flow methods in most experiments we conducted, resulting in lower FID scores.

To make reinforcement learning more sample efficient, we need better credit assignment methods that measure an action's influence on future rewards. Building upon Hindsight Credit Assignment (HCA), we introduce Counterfactual Contribution Analysis (COCOA), a new family of model-based credit assignment algorithms. Our algorithms achieve precise credit assignment by measuring the contribution of actions upon obtaining subsequent rewards, by quantifying a counterfactual query: 'Would the agent still have reached this reward if it had taken another action?'. We show that measuring contributions w.r.t. rewarding states, as is done in HCA, results in spurious estimates of contributions, causing HCA to degrade towards the high-variance REINFORCE estimator in many relevant environments. Instead, we measure contributions w.r.t. rewards or learned representations of the rewarding objects, resulting in gradient estimates with lower variance. We run experiments on a suite of problems specifically designed to evaluate long-term credit assignment capabilities. By using dynamic programming, we measure ground-truth policy gradients and show that the improved performance of our new model-based credit assignment methods is due to lower bias and variance compared to HCA and common baselines. Our results demonstrate how modeling action contributions towards rewarding outcomes can be leveraged for credit assignment, opening a new path towards sample-efficient reinforcement learning.

Researchers in explainable artificial intelligence have developed numerous methods for helping users understand the predictions of complex supervised learning models. By contrast, explaining the $\textit{uncertainty}$ of model outputs has received relatively little attention. We adapt the popular Shapley value framework to explain various types of predictive uncertainty, quantifying each feature's contribution to the conditional entropy of individual model outputs. We consider games with modified characteristic functions and find deep connections between the resulting Shapley values and fundamental quantities from information theory and conditional independence testing. We outline inference procedures for finite sample error rate control with provable guarantees, and implement efficient algorithms that perform well in a range of experiments on real and simulated data. Our method has applications to covariate shift detection, active learning, feature selection, and active feature-value acquisition.

Additive Noise Models (ANMs) are a common model class for causal discovery from observational data and are often used to generate synthetic data for causal discovery benchmarking. Specifying an ANM requires choosing all parameters, including those not fixed by explicit assumptions. Reisach et al. (2021) show that sorting variables by increasing variance often yields an ordering close to a causal order and introduce var-sortability to quantify this alignment. Since increasing variances may be unrealistic and are scale-dependent, ANM data are often standardized in benchmarks. We show that synthetic ANM data are characterized by another pattern that is scale-invariant: the explainable fraction of a variable's variance, as captured by the coefficient of determination $R^2$, tends to increase along the causal order. The result is high $R^2$-sortability, meaning that sorting the variables by increasing $R^2$ yields an ordering close to a causal order. We propose an efficient baseline algorithm termed $R^2$-SortnRegress that exploits high $R^2$-sortability and that can match and exceed the performance of established causal discovery algorithms. We show analytically that sufficiently high edge weights lead to a relative decrease of the noise contributions along causal chains, resulting in increasingly deterministic relationships and high $R^2$. We characterize $R^2$-sortability for different simulation parameters and find high values in common settings. Our findings reveal high $R^2$-sortability as an assumption about the data generating process relevant to causal discovery and implicit in many ANM sampling schemes. It should be made explicit, as its prevalence in real-world data is unknown. For causal discovery benchmarking, we implement $R^2$-sortability, the $R^2$-SortnRegress algorithm, and ANM simulation procedures in our library CausalDisco at https://causaldisco.github.io/CausalDisco/.

Positive and unlabelled learning is an important problem which arises naturally in many applications. The significant limitation of almost all existing methods lies in assuming that the propensity score function is constant (SCAR assumption), which is unrealistic in many practical situations. Avoiding this assumption, we consider parametric approach to the problem of joint estimation of posterior probability and propensity score functions. We show that under mild assumptions when both functions have the same parametric form (e.g. logistic with different parameters) the corresponding parameters are identifiable. Motivated by this, we propose two approaches to their estimation: joint maximum likelihood method and the second approach based on alternating maximization of two Fisher consistent expressions. Our experimental results show that the proposed methods are comparable or better than the existing methods based on Expectation-Maximisation scheme.

Gibbs samplers [12] are a family of Markov Chain Monte Carlo (MCMC) algorithms [10] commonly used in various scientific fields. In the context of Bayesian Statistics, they are routinely employed to draw samples from posterior distributions of unknown parameters conditional to the observed data [28, 37]. Like most MCMC methods, they are guaranteed to converge to the correct posterior distribution as the number of iterations tends to infinity under mild assumptions [54]. However, understanding how quickly this convergence occurs, for example by quantifying the so-called mixing time of the Markov chain generated by the algorithm, is in general a hard task. In this paper we address this question for Gibbs samplers targeting certain classes of high-dimensional Bayesian hierarchical models. Analysing convergence properties, such as mixing times, is the key technical step needed to rigorously quantify the computational cost of MCMC algorithms.

Optimal topology synthesis is generally resource-intensive and time-consuming to be done in real time for large ad-hoc robot networks. One should only perform topology re-computations if the probability of topology recoverability after the occurrence of any fault surpasses that of its irrecoverability. We formulate this problem as a binary classification problem. Then, we develop a two-pathway data-driven model based on Bayesian Gaussian mixture models that predicts the solution to a typical problem by two different pre-fault and post-fault prediction pathways. The results, obtained by the integration of the predictions of those pathways, clearly indicate the success of our model in solving the topology (ir)recoverability prediction problem compared to the best of current strategies found in the literature.

Reconstructing astrophysical and cosmological fields from observations is challenging. It requires accounting for non-linear transformations, mixing of spatial structure, and noise. In contrast, forward simulators that map fields to observations are readily available for many applications. We present a versatile Bayesian field reconstruction algorithm rooted in simulation-based inference and enhanced by autoregressive modeling. The proposed technique is applicable to generic (non-differentiable) forward simulators and allows sampling from the posterior for the underlying field. We show first promising results on a proof-of-concept application: the recovery of cosmological initial conditions from late-time density fields.

In today's world, the risk of emerging and re-emerging epidemics have increased. The recent advancement in healthcare technology has made it possible to predict an epidemic outbreak in a region. Early prediction of an epidemic outbreak greatly helps the authorities to be prepared with the necessary medications and logistics required to keep things in control. In this article, we try to predict the epidemic outbreak (influenza, hepatitis and malaria) for the state of New York, USA using machine and deep learning algorithms, and a portal has been created for the same which can alert the authorities and health care organisations of the region in case of an outbreak. The algorithm takes historical data to predict the possible number of cases for 5 weeks into the future. Non-clinical factors like google search trends, social media data and weather data have also been used to predict the probability of an outbreak. Keywords: Epidemic, Clinical analysis, LSTM, ARIMA Introduction More than six different influenza pandemics and epidemics have struck in just a century. Every year nearly 500,000 people die due to seasonal influenza and other epidemics. Even with the advancement of technology, particularly in the healthcare industry, it is impossible to prevent an outbreak, but it's possible to be prepared for one. With the help of machine learning, we can now monitor and forecast the expected number of cases of a given disease for a particular region by using meteorological data, social media data, and historical data. This would be extremely useful for the health care centres and pharmacies of a particular region to be prepared in advance and stock up their inventory if needed. As seen in India during the second wave of COVID-19, due to the suddenness of the outbreak there was an unprecedented demand in healthcare resources from medicines, beds, etc. Such unexpected epidemic or pandemic outbreaks threaten to overwhelm the healthcare system of any region. But knowing the possibility of an outbreak beforehand helps the healthcare system to be prepared in advance, as it gives them enough time to accumulate the necessary items like medicines, oxygen cylinders, etc.

Sentiment analysis (SA) is commonly applied to digital textual data, revealing insight into opinions and feelings. Many systematic reviews have summarized existing work, but often overlook discussions of validity and scientific practices. Here, we present an overview of reviews, synthesizing 38 systematic reviews, containing 2,275 primary studies. We devise a bespoke quality assessment framework designed to assess the rigor and quality of systematic review methodologies and reporting standards. Our findings show diverse applications and methods, limited reporting rigor, and challenges over time. We discuss how future research and practitioners can address these issues and highlight their importance across numerous applications.