We introduce a novel, probabilistic binary latent variable model to detect noisy or approximate repeats of patterns in sparse binary data. The model is based on the "Noisy-OR model" (Heckerman, 1990), used previously for disease and topic modelling. The model's capability is demonstrated by extracting structure in recordings from retinal neurons, but it can be widely applied to discover and model latent structure in noisy binary data. In the context of spiking neural data, the task is to "explain" spikes of individual neurons in terms of groups of neurons, "Cell Assemblies" (CAs), that often fire together, due to mutual interactions or other causes. The model infers sparse activity in a set of binary latent variables, each describing the activity of a cell assembly. When the latent variable of a cell assembly is active, it reduces the probabilities of neurons belonging to this assembly to be inactive. The conditional probability kernels of the latent components are learned from the data in an expectation maximization scheme, involving inference of latent states and parameter adjustments to the model. We thoroughly validate the model on synthesized spike trains constructed to statistically resemble recorded retinal responses to white noise stimulus and natural movie stimulus in data. We also apply our model to spiking responses recorded in retinal ganglion cells (RGCs) during stimulation with a movie and discuss the found structure.

We revisit the theory of importance weighted variational inference (IWVI), a promising strategy for learning latent variable models. IWVI uses new variational bounds, known as Monte Carlo objectives (MCOs), obtained by replacing intractable integrals by Monte Carlo estimates -- usually simply obtained via importance sampling. Burda, Grosse and Salakhutdinov (2016) showed that increasing the number of importance samples provably tightens the gap between the bound and the likelihood. Inspired by this simple monotonicity theorem, we present a series of nonasymptotic results that link properties of Monte Carlo estimates to tightness of MCOs. We challenge the rationale that smaller Monte Carlo variance leads to better bounds. We confirm theoretically the empirical findings of several recent papers by showing that, in a precise sense, negative correlation reduces the variational gap. We also generalise the original monotonicity theorem by considering non-uniform weights. We discuss several practical consequences of our theoretical results. Our work borrows many ideas and results from the theory of stochastic orders.

Explainable artificial intelligence (XAI) aims to make learning machines less opaque, and offers researchers and practitioners various tools to reveal the decision-making strategies of neural networks. In this work, we investigate how XAI methods can be used for exploring and visualizing the diversity of feature representations learned by Bayesian neural networks (BNNs). Our goal is to provide a global understanding of BNNs by making their decision-making strategies a) visible and tangible through feature visualizations and b) quantitatively measurable with a distance measure learned by contrastive learning. Our work provides new insights into the posterior distribution in terms of human-understandable feature information with regard to the underlying decision-making strategies. Our main findings are the following: 1) global XAI methods can be applied to explain the diversity of decision-making strategies of BNN instances, 2) Monte Carlo dropout exhibits increased diversity in feature representations compared to the multimodal posterior approximation of MultiSWAG, 3) the diversity of learned feature representations highly correlates with the uncertainty estimates, and 4) the inter-mode diversity of the multimodal posterior decreases as the network width increases, while the intra-mode diversity increases. Our findings are consistent with the recent deep neural networks theory, providing additional intuitions about what the theory implies in terms of humanly understandable concepts.

The Expectation-Maximization (EM) algorithm is a way to find maximum-likelihood estimates for model parameters when the data is incomplete, or has missing data points, or has unobserved/hidden latent variables. This is an iterative way to approximate the maximum likelihood function. While maximum likelihood estimation can find the "best fit" model for a set of data, it does not work specifically well for incomplete data sets. The more complex Expectation-Maximization (EM) algorithm can find model parameters even if you have missing data. It works by selecting random values for the missing data points and using those guesses to estimate a second set of data.

In today's world, Machine learning becomes one of the popular and exciting fields of study that gives machines the ability to learn and become more accurate at predicting outcomes for the unseen data i.e, not seen the data in prior. The ideas in Machine learning overlaps and receives from Artificial Intelligence and many other related technologies. Today, machine learning is evolved from Pattern Recognition and the concept that computers can learn without being explicitly programmed to performing specific tasks. We can use the Machine Learning algorithms(e.g, Machine learning models can be classified into two types of models – Discriminative and Generative models.

We study the optimal sample complexity of learning a Gaussian directed acyclic graph (DAG) from observational data. Our main result establishes the minimax optimal sample complexity for learning the structure of a linear Gaussian DAG model with equal variances to be $n\asymp q\log(d/q)$, where $q$ is the maximum number of parents and $d$ is the number of nodes. We further make comparisons with the classical problem of learning (undirected) Gaussian graphical models, showing that under the equal variance assumption, these two problems share the same optimal sample complexity. In other words, at least for Gaussian models with equal error variances, learning a directed graphical model is not more difficult than learning an undirected graphical model. Our results also extend to more general identification assumptions as well as subgaussian errors.

A new generation of increasingly autonomous and self-learning cyber-physical systems (CPS) is being developed for control applications in the real world. These systems are AI-based in that they leverage techniques from the field of Artificial intelligence (AI) to flexibly cope with imprecision, inconsistency, incompleteness, to have an inherent ability to learn from experience, and to adapt according to changing and even unforeseen situations. This extra flexibility of AI systems makes it harder to predict their behavior. Moreover, AI systems usually are safety-critical in that they may be causing real harm in (and to) the real world. Consequently, the central question regarding the development of such systems is how to handle or even overcome this basic dichotomy between unpredictable and safe behavior of AI systems. In other words, how can we best construct systems that exploit AI techniques, without incurring the frailties of "AI-like" behavior?

Interval-valued information systems are generalized models of single-valued information systems. By rough set approach, interval-valued information systems have been extensively studied. Authors could establish many binary relations from the same interval-valued information system. In this paper, we do some researches on comparing these binary relations so as to provide numerical scales for choosing suitable relations in dealing with interval-valued information systems. Firstly, based on similarity degrees, we compare the most common three binary relations induced from the same interval-valued information system. Secondly, we propose the concepts of transitive degree and cluster degree, and investigate their properties. Finally, we provide some methods to compare binary relations by means of the transitive degree and the cluster degree. Furthermore, we use these methods to analyze the most common three relations induced from Face Recognition Dataset, and obtain that $RF_{B} ^{\lambda}$ is a good choice when we deal with an interval-valued information system by means of rough set approach.

We study the problem of learning the preferences of drivers and planners in the context of last mile delivery. Given a data set containing historical decisions and delivery locations, the goal is to capture the implicit preferences of the decision-makers. We consider two ways to use the historical data: one is through a probability estimation method that learns transition probabilities between stops (or zones). This is a fast and accurate method, recently studied in a VRP setting. Furthermore, we explore the use of machine learning to infer how to best balance multiple objectives such as distance, probability and penalties. Specifically, we cast the learning problem as a structured output prediction problem, where training is done by repeatedly calling the TSP solver. Another important aspect we consider is that for last-mile delivery, every address is a potential client and hence the data is very sparse. Hence, we propose a two-stage approach that first learns preferences at the zone level in order to compute a zone routing; after which a penalty-based TSP computes the stop routing. Results show that the zone transition probability estimation performs well, and that the structured output prediction learning can improve the results further. We hence showcase a successful combination of both probability estimation and machine learning, all the while using standard TSP solvers, both during learning and to compute the final solution; this means the methodology is applicable to other, real-life, TSP variants, or proprietary solvers.

As the costs of sensors and associated IT infrastructure decreases - as exemplified by the Internet of Things - increasing volumes of observational data are becoming available for use by environmental scientists. However, as the number of available observation sites increases, so too does the opportunity for data quality issues to emerge, particularly given that many of these sensors do not have the benefit of official maintenance teams. To realise the value of crowd sourced 'Internet of Things' type observations for environmental modelling, we require approaches that can automate the detection of outliers during the data modelling process so that they do not contaminate the true distribution of the phenomena of interest. To this end, here we present a Bayesian deep learning approach for spatio-temporal modelling of environmental variables with automatic outlier detection. Our approach implements a Gaussian-uniform mixture density network whose dual purposes - modelling the phenomenon of interest, and learning to classify and ignore outliers - are achieved simultaneously, each by specifically designed branches of our neural network. For our example application, we use the Met Office's Weather Observation Website data, an archive of observations from around 1900 privately run and unofficial weather stations across the British Isles. Using data on surface air temperature, we demonstrate how our deep mixture model approach enables the modelling of a highly skilled spatio-temporal temperature distribution without contamination from spurious observations. We hope that adoption of our approach will help unlock the potential of incorporating a wider range of observation sources, including from crowd sourcing, into future environmental models.