Given a Boolean formula and a functions assigning weights to assignments of values to the Boolean variable, we consider the problems of Weighted Constrained Sampling (WCS) and Weighted Model Counting (WMC). The first, also called distributionaware sampling (Chakraborty et al, 2014), involves sampling assignments to the Boolean variables with a probability proportional to their weight given that the formula is satisfied. The latter (Sang et al, 2005) consists in computing the sum of the weights of the models of the formula, i.e. the weighted model count. WCS has important applications in a variety of domanis, including statistical physics (Jerrum and Sinclair, 1996), statistics (Madras and Piccioni, 1999), hardware verification (Naveh et al, 2006), and probabilistic reasoning, where it can be used to solve the problem of Most Probable Explanation (MPE) and Maximum A Posteriori (MAP). MPE (Sang et al, 2007) involves finding an assignment to all variables that satisfies a Boolean formula and has the maximum weight. The related MAP problem means finding an assignment of a subset of the variables such that the sum of the weights of the models of the formula that agree on the assignment is maximum. WMC was successfully applied, among others, to the problem of performing inference in graphical models (Chavira and Darwiche, 2008; Sang et al, 2005).

For one to guarantee higher-quality software development processes, risk management is essential. Furthermore, risks are those that could negatively impact an organization's operations or a project's progress. The appropriate prioritisation of software project risks is a crucial factor in ascertaining the software project's performance features and eventual success. They can be used harmoniously with the same training samples and have good complement and compatibility. We carried out in-depth tests on four benchmark datasets to confirm the efficacy of our CIA approach in closed-world and open-world scenarios, with and without defence. We also present a sequential augmentation parameter optimisation technique that captures the interdependencies of the latest deep learning state-of-the-art WF attack models. To achieve precise software risk assessment, the enhanced crow search algorithm (ECSA) is used to modify the ANFIS settings. Solutions that very slightly alter the local optimum and stay inside it are extracted using the ECSA. ANFIS variable when utilising the ANFIS technique. An experimental validation with NASA 93 dataset and 93 software project values was performed. This method's output presents a clear image of the software risk elements that are essential to achieving project performance. The results of our experiments show that, when compared to other current methods, our integrative fuzzy techniques may perform more accurately and effectively in the evaluation of software project risks.

In many real-world settings, an agent must learn to act in environments where no reward signal can be specified, but a set of expert demonstrations is available. Imitation learning (IL) is a popular framework for learning policies from such demonstrations. However, in some cases, differences in observability between the expert and the agent can give rise to an imitation gap such that the expert's policy is not optimal for the agent and a naive application of IL can fail catastrophically. In particular, if the expert observes the Markov state and the agent does not, then the expert will not demonstrate the information-gathering behavior needed by the agent but not the expert. In this paper, we propose a Bayesian solution to the Imitation Gap (BIG), first using the expert demonstrations, together with a prior specifying the cost of exploratory behavior that is not demonstrated, to infer a posterior over rewards with Bayesian inverse reinforcement learning (IRL). BIG then uses the reward posterior to learn a Bayes-optimal policy. Our experiments show that BIG, unlike IL, allows the agent to explore at test time when presented with an imitation gap, whilst still learning to behave optimally using expert demonstrations when no such gap exists.

Mastering multiple tasks through exploration and learning in an environment poses a significant challenge in reinforcement learning (RL). Unsupervised RL has been introduced to address this challenge by training policies with intrinsic rewards rather than extrinsic rewards. However, current intrinsic reward designs and unsupervised RL algorithms often overlook the heterogeneous nature of collected samples, thereby diminishing their sample efficiency. To overcome this limitation, in this paper, we propose a reward-free RL algorithm called \alg. The key idea behind our algorithm is an uncertainty-aware intrinsic reward for exploring the environment and an uncertainty-weighted learning process to handle heterogeneous uncertainty in different samples. Theoretically, we show that in order to find an $\epsilon$-optimal policy, GFA-RFE needs to collect $\tilde{O} (H^2 \log N_{\mathcal F} (\epsilon) \mathrm{dim} (\mathcal F) / \epsilon^2 )$ number of episodes, where $\mathcal F$ is the value function class with covering number $N_{\mathcal F} (\epsilon)$ and generalized eluder dimension $\mathrm{dim} (\mathcal F)$. Such a result outperforms all existing reward-free RL algorithms. We further implement and evaluate GFA-RFE across various domains and tasks in the DeepMind Control Suite. Experiment results show that GFA-RFE outperforms or is comparable to the performance of state-of-the-art unsupervised RL algorithms.

Estimating treatment effects over time holds significance in various domains, including precision medicine, epidemiology, economy, and marketing. This paper introduces a unique approach to counterfactual regression over time, emphasizing long-term predictions. Distinguishing itself from existing models like Causal Transformer, our approach highlights the efficacy of employing RNNs for long-term forecasting, complemented by Contrastive Predictive Coding (CPC) and Information Maximization (InfoMax). Emphasizing efficiency, we avoid the need for computationally expensive transformers. Leveraging CPC, our method captures long-term dependencies in the presence of time-varying confounders. Notably, recent models have disregarded the importance of invertible representation, compromising identification assumptions. To remedy this, we employ the InfoMax principle, maximizing a lower bound of mutual information between sequence data and its representation. Our method achieves state-of-the-art counterfactual estimation results using both synthetic and real-world data, marking the pioneering incorporation of Contrastive Predictive Encoding in causal inference.

International Journal of Forecasting, 2024.], a generalised exponential smoothing model was proposed that is able to capture strong trends and volatility in time series. This method achieved state-of-the-art performance in many forecasting tasks, but its fitting proce dure, which is based on the NUTS sampler, is very computationally expensive. In this work, w e propose several modifications to the original model, as well as a bespoke Gibbs sampler for p osterior exploration; these changes improve sampling time by an order of magnitude, thus rendering the model much more practically relevant. The new model, and sampler, are evalu ated on the M3 dataset and are shown to be competitive, or superior, in terms of accuracy to the original method, while being substantially faster to run.

A new particle-based sampling and approximate inference method, based on electrostatics and Newton mechanics principles, is introduced with theoretical ground, algorithm design and experimental validation. This method simulates an interacting particle system (IPS) where particles, i.e. the freely-moving negative charges and spatially-fixed positive charges with magnitudes proportional to the target distribution, interact with each other via attraction and repulsion induced by the resulting electric fields described by Poisson's equation. The IPS evolves towards a steady-state where the distribution of negative charges conforms to the target distribution. This physics-inspired method offers deterministic, gradient-free sampling and inference, achieving comparable performance as other particle-based and MCMC methods in benchmark tasks of inferring complex densities, Bayesian logistic regression and dynamical system identification. A discrete-time, discrete-space algorithmic design, readily extendable to continuous time and space, is provided for usage in more general inference problems occurring in probabilistic machine learning scenarios such as Bayesian inference, generative modelling, and beyond.

Dynamic Bayesian Networks (DBNs) are a class of Probabilistic Graphical Models that enable the modeling of a Markovian dynamic process through defining the kernel transition by the DAG structure of the graph found to fit a dataset. There are a number of structure learners than enable one to find the structure of a DBN to fit data, each of which with its own set of particular advantages and disadvantages. The structure of a DBN itself presents transparent criteria in order to identify causal discovery between variables. However, without the presence of large quantities of data, identifying a ground truth causal structure becomes unrealistic in practice. However, one can consider a procedure by which a set of graphs identifying structure are computed as approximate noisy solutions, and subsequently amortized in a broader statistical procedure fitting a mixture of DBNs. Each component of the mixture presents an alternative hypothesis on the causal structure. From the mixture weights, one can also compute the Bayes Factors comparing the preponderance of evidence between different models. This presents a natural opportunity for the development of Empirical Bayesian methods.

Reinforcement Learning (RL) has gained significant attention across various domains. However, the increasing complexity of RL programs presents testing challenges, particularly the oracle problem: defining the correctness of the RL program. Conventional human oracles struggle to cope with the complexity, leading to inefficiencies and potential unreliability in RL testing. To alleviate this problem, we propose an automated oracle approach that leverages RL properties using fuzzy logic. Our oracle quantifies an agent's behavioral compliance with reward policies and analyzes its trend over training episodes. It labels an RL program as "Buggy" if the compliance trend violates expectations derived from RL characteristics. We evaluate our oracle on RL programs with varying complexities and compare it with human oracles. Results show that while human oracles perform well in simpler testing scenarios, our fuzzy oracle demonstrates superior performance in complex environments. The proposed approach shows promise in addressing the oracle problem for RL testing, particularly in complex cases where manual testing falls short. It offers a potential solution to improve the efficiency, reliability, and scalability of RL program testing. This research takes a step towards automated testing of RL programs and highlights the potential of fuzzy logic-based oracles in tackling the oracle problem.

We study submodular optimization in adversarial context, applicable to machine learning problems such as feature selection using data susceptible to uncertainties and attacks. We focus on Stackelberg games between an attacker (or interdictor) and a defender where the attacker aims to minimize the defender's objective of maximizing a $k$-submodular function. We allow uncertainties arising from the success of attacks and inherent data noise, and address challenges due to incomplete knowledge of the probability distribution of random parameters. Specifically, we introduce Distributionally Risk-Averse $k$-Submodular Interdiction Problem (DRA $k$-SIP) and Distributionally Risk-Receptive $k$-Submodular Interdiction Problem (DRR $k$-SIP) along with finitely convergent exact algorithms for solving them. The DRA $k$-SIP solution allows risk-averse interdictor to develop robust strategies for real-world uncertainties. Conversely, DRR $k$-SIP solution suggests aggressive tactics for attackers, willing to embrace (distributional) risk to inflict maximum damage, identifying critical vulnerable components, which can be used for the defender's defensive strategies. The optimal values derived from both DRA $k$-SIP and DRR $k$-SIP offer a confidence interval-like range for the expected value of the defender's objective function, capturing distributional ambiguity. We conduct computational experiments using instances of feature selection and sensor placement problems, and Wisconsin breast cancer data and synthetic data, respectively.