We introduce GEDI, a Bayesian framework that combines existing self-supervised learning objectives with likelihood-based generative models. This framework leverages the benefits of both GEnerative and DIscriminative approaches, resulting in improved symbolic representations over standalone solutions. Additionally, GEDI can be easily integrated and trained jointly with existing neuro-symbolic frameworks without the need for additional supervision or costly pre-training steps. We demonstrate through experiments on real-world data, including SVHN, CIFAR10, and CIFAR100, that GEDI outperforms existing self-supervised learning strategies in terms of clustering performance by a significant margin. The symbolic component further allows it to leverage knowledge in the form of logical constraints to improve performance in the small data regime.

Customer churn describes terminating a relationship with a business or reducing customer engagement over a specific period. Customer acquisition cost can be five to six times that of customer retention, hence investing in customers with churn risk is wise. Causal analysis of the churn model can predict whether a customer will churn in the foreseeable future and identify effects and possible causes for churn. In general, this study presents a conceptual framework to discover the confounding features that correlate with independent variables and are causally related to those dependent variables that impact churn. We combine different algorithms including the SMOTE, ensemble ANN, and Bayesian networks to address churn prediction problems on a massive and high-dimensional finance data that is usually generated in financial institutions due to employing interval-based features used in Customer Relationship Management systems. The effects of the curse and blessing of dimensionality assessed by utilising the Recursive Feature Elimination method to overcome the high dimension feature space problem. Moreover, a causal discovery performed to find possible interpretation methods to describe cause probabilities that lead to customer churn. Evaluation metrics on validation data confirm the random forest and our ensemble ANN model, with %86 accuracy, outperformed other approaches. Causal analysis results confirm that some independent causal variables representing the level of super guarantee contribution, account growth, and account balance amount were identified as confounding variables that cause customer churn with a high degree of belief. This article provides a real-world customer churn analysis from current status inference to future directions in local superannuation funds.

Traffic congestion caused by non-recurring incidents such as vehicle crashes and debris is a key issue for Traffic Management Centers (TMCs). Clearing incidents in a timely manner is essential for improving safety and reducing delays and emissions for the traveling public. However, TMCs and other responders face a challenge in predicting the duration of incidents (until the roadway is clear), making decisions of what resources to deploy difficult. To address this problem, this research developed an analytical framework and end-to-end machine-learning solution for predicting incident duration based on information available as soon as an incident report is received. Quality predictions of incident duration can help TMCs and other responders take a proactive approach in deploying responder services such as tow trucks, maintenance crews or activating alternative routes. The predictions use a combination of classification and regression machine learning modules. The performance of the developed solution has been evaluated based on the Mean Absolute Error (MAE), or deviation from the actual incident duration as well as Area Under the Curve (AUC) and Mean Absolute Percentage Error (MAPE). The results showed that the framework significantly improved incident duration prediction compared to methods from previous research.

Along with Markov chain Monte Carlo (MCMC) methods, variational inference (VI) has emerged as a central computational approach to large-scale Bayesian inference. Rather than sampling from the true posterior $\pi$, VI aims at producing a simple but effective approximation $\hat \pi$ to $\pi$ for which summary statistics are easy to compute. However, unlike the well-studied MCMC methodology, algorithmic guarantees for VI are still relatively less well-understood. In this work, we propose principled methods for VI, in which $\hat \pi$ is taken to be a Gaussian or a mixture of Gaussians, which rest upon the theory of gradient flows on the Bures--Wasserstein space of Gaussian measures. Akin to MCMC, it comes with strong theoretical guarantees when $\pi$ is log-concave.

We propose a new type of multi-agent interactive classifier that provides provable interpretability guarantees even for complex agents such as neural networks. These guarantees consist of bounds on the mutual information of the features selected by this classifier. Our results are inspired by the Merlin-Arthur protocol from Interactive Proof Systems and express these bounds in terms of measurable metrics such as soundness and completeness. Compared to existing interactive setups we do not rely on optimal agents or on the assumption that features are distributed independently. Instead, we use the relative strength of the agents as well as the new concept of Asymmetric Feature Correlation which captures the precise kind of correlations that make interpretability guarantees difficult. %relates the information carried by sets of features to one of the individual features. We test our results through numerical experiments on two small-scale datasets where high mutual information can be verified explicitly.

This paper introduces a stochastic plug-and-play (PnP) sampling algorithm that leverages variable splitting to efficiently sample from a posterior distribution. The algorithm based on split Gibbs sampling (SGS) draws inspiration from the alternating direction method of multipliers (ADMM). It divides the challenging task of posterior sampling into two simpler sampling problems. The first problem depends on the likelihood function, while the second is interpreted as a Bayesian denoising problem that can be readily carried out by a deep generative model. Specifically, for an illustrative purpose, the proposed method is implemented in this paper using state-of-the-art diffusion-based generative models. Akin to its deterministic PnP-based counterparts, the proposed method exhibits the great advantage of not requiring an explicit choice of the prior distribution, which is rather encoded into a pre-trained generative model. However, unlike optimization methods (e.g., PnP-ADMM) which generally provide only point estimates, the proposed approach allows conventional Bayesian estimators to be accompanied by confidence intervals at a reasonable additional computational cost. Experiments on commonly studied image processing problems illustrate the efficiency of the proposed sampling strategy. Its performance is compared to recent state-of-the-art optimization and sampling methods.

Bayesian models are a powerful tool for studying complex data, allowing the analyst to encode rich hierarchical dependencies and leverage prior information. Most importantly, they facilitate a complete characterization of uncertainty through the posterior distribution. Practical posterior computation is commonly performed via MCMC, which can be computationally infeasible for high dimensional models with many observations. In this article we discuss the potential to improve posterior computation using ideas from machine learning. Concrete future directions are explored in vignettes on normalizing flows, Bayesian coresets, distributed Bayesian inference, and variational inference.

We introduce a new approach to probabilistic unsupervised learning based on the recognition-parametrised model (RPM): a normalised semi-parametric hypothesis class for joint distributions over observed and latent variables. Under the key assumption that observations are conditionally independent given latents, the RPM combines parametric prior and observation-conditioned latent distributions with non-parametric observation marginals. This approach leads to a flexible learnt recognition model capturing latent dependence between observations, without the need for an explicit, parametric generative model. The RPM admits exact maximum-likelihood learning for discrete latents, even for powerful neural-network-based recognition. We develop effective approximations applicable in the continuous-latent case. Experiments demonstrate the effectiveness of the RPM on high-dimensional data, learning image classification from weak indirect supervision; direct image-level latent Dirichlet allocation; and recognition-parametrised Gaussian process factor analysis (RP-GPFA) applied to multi-factorial spatiotemporal datasets. The RPM provides a powerful framework to discover meaningful latent structure underlying observational data, a function critical to both animal and artificial intelligence.

Deep neural networks (DNNs) have received tremendous attention and achieved great success in various applications, such as image and video analysis, natural language processing, recommendation systems, and drug discovery. However, inherent uncertainties derived from different root causes have been realized as serious hurdles for DNNs to find robust and trustworthy solutions for real-world problems. A lack of consideration of such uncertainties may lead to unnecessary risk. For example, a self-driving autonomous car can misdetect a human on the road. A deep learning-based medical assistant may misdiagnose cancer as a benign tumor. In this work, we study how to measure different uncertainty causes for DNNs and use them to solve diverse decision-making problems more effectively. In the first part of this thesis, we develop a general learning framework to quantify multiple types of uncertainties caused by different root causes, such as vacuity (i.e., uncertainty due to a lack of evidence) and dissonance (i.e., uncertainty due to conflicting evidence), for graph neural networks. We provide a theoretical analysis of the relationships between different uncertainty types. We further demonstrate that dissonance is most effective for misclassification detection and vacuity is most effective for Out-of-Distribution (OOD) detection. In the second part of the thesis, we study the significant impact of OOD objects on semi-supervised learning (SSL) for DNNs and develop a novel framework to improve the robustness of existing SSL algorithms against OODs. In the last part of the thesis, we create a general learning framework to quantity multiple uncertainty types for multi-label temporal neural networks. We further develop novel uncertainty fusion operators to quantify the fused uncertainty of a subsequence for early event detection.

There are a variety of features of the human voice that can be classified as pitch, timbre, loudness, and vocal tone. It is observed in numerous incidents that human expresses their feelings using different vocal qualities when they are speaking. The primary objective of this research is to recognize different emotions of human beings such as anger, sadness, fear, neutrality, disgust, pleasant surprise, and happiness by using several MATLAB functions namely, spectral descriptors, periodicity, and harmonicity. To accomplish the work, we analyze the CREMA-D (Crowd-sourced Emotional Multimodal Actors Data) & TESS (Toronto Emotional Speech Set) datasets of human speech. The audio file contains data that have various characteristics (e.g., noisy, speedy, slow) thereby the efficiency of the ML (Machine Learning) models increases significantly. The EMD (Empirical Mode Decomposition) is utilized for the process of signal decomposition. Then, the features are extracted through the use of several techniques such as the MFCC, GTCC, spectral centroid, roll-off point, entropy, spread, flux, harmonic ratio, energy, skewness, flatness, and audio delta. The data is trained using some renowned ML models namely, Support Vector Machine, Neural Network, Ensemble, and KNN. The algorithms show an accuracy of 67.7%, 63.3%, 61.6%, and 59.0% respectively for the test data and 77.7%, 76.1%, 99.1%, and 61.2% for the training data. We have conducted experiments using Matlab and the result shows that our model is very prominent and flexible than existing similar works.