In recent times, a considerable number of research studies have been carried out to address the issue of Missing Value Imputation (MVI). MVI aims to provide a primary solution for datasets that have one or more missing attribute values. The advancements in Artificial Intelligence (AI) drive the development of new and improved machine learning (ML) algorithms and methods. The advancements in ML have opened up significant opportunities for effectively imputing these missing values. The main objective of this article is to conduct a comprehensive and rigorous review, as well as analysis, of the state-of-the-art ML applications in MVI methods. This analysis seeks to enhance researchers' understanding of the subject and facilitate the development of robust and impactful interventions in data preprocessing for Data Analytics. The review is performed following the Preferred Reporting Items for Systematic Reviews and Meta-Analysis (PRISMA) technique. More than 100 articles published between 2014 and 2023 are critically reviewed, considering the methods and findings. Furthermore, the latest literature is examined to scrutinize the trends in MVI methods and their evaluation. The accomplishments and limitations of the existing literature are discussed in detail. The survey concludes by identifying the current gaps in research and providing suggestions for future research directions and emerging trends in related fields of interest.

A crucial capability of Machine Learning models in real-world applications is the ability to continuously learn new tasks. This adaptability allows them to respond to potentially inevitable shifts in the data-generating distribution over time. However, in Continual Learning (CL) settings, models often struggle to balance learning new tasks (plasticity) with retaining previous knowledge (memory stability). Consequently, they are susceptible to Catastrophic Forgetting, which degrades performance and undermines the reliability of deployed systems. Variational Continual Learning methods tackle this challenge by employing a learning objective that recursively updates the posterior distribution and enforces it to stay close to the latest posterior estimate. Nonetheless, we argue that these methods may be ineffective due to compounding approximation errors over successive recursions. To mitigate this, we propose new learning objectives that integrate the regularization effects of multiple previous posterior estimations, preventing individual errors from dominating future posterior updates and compounding over time. We reveal insightful connections between these objectives and Temporal-Difference methods, a popular learning mechanism in Reinforcement Learning and Neuroscience. We evaluate the proposed objectives on challenging versions of popular CL benchmarks, demonstrating that they outperform standard Variational CL methods and non-variational baselines, effectively alleviating Catastrophic Forgetting.

Solar irradiance forecasts can be dynamic and unreliable due to changing weather conditions. Near the Arctic circle, this also translates into a distinct set of further challenges. This work is forecasting solar irradiance with Norwegian data using variations of Long-Short-Term Memory units (LSTMs). In order to gain more trustworthiness of results, the probabilistic approaches Quantile Regression (QR) and Maximum Likelihood (MLE) are optimized on top of the LSTMs, providing measures of uncertainty for the results. MLE is further extended by using a Johnson's SU distribution, a Johnson's SB distribution, and a Weibull distribution in addition to a normal Gaussian to model parameters. Contrary to a Gaussian, Weibull, Johnson's SU and Johnson's SB can return skewed distributions, enabling it to fit the non-normal solar irradiance distribution more optimally. The LSTMs are compared against each other, a simple Multi-layer Perceptron (MLP), and a smart-persistence estimator. The proposed LSTMs are found to be more accurate than smart persistence and the MLP for a multi-horizon, day-ahead (36 hours) forecast. The deterministic LSTM showed better root mean squared error (RMSE), but worse mean absolute error (MAE) than a MLE with Johnson's SB distribution. Probabilistic uncertainty estimation is shown to fit relatively well across the distribution of observed irradiance. While QR shows better uncertainty estimation calibration, MLE with Johnson's SB, Johnson's SU, or Gaussian show better performance in the other metrics employed. Optimizing and comparing the models against each other reveals a seemingly inherent trade-off between point-prediction and uncertainty estimation calibration.

Symmetries have proven useful in machine learning models, improving generalisation and overall performance. At the same time, recent advancements in learning dynamical systems rely on modelling the underlying Hamiltonian to guarantee the conservation of energy. These approaches can be connected via a seminal result in mathematical physics: Noether's theorem, which states that symmetries in a dynamical system correspond to conserved quantities. This work uses Noether's theorem to parameterise symmetries as learnable conserved quantities. We then allow conserved quantities and associated symmetries to be learned directly from train data through approximate Bayesian model selection, jointly with the regular training procedure. As training objective, we derive a variational lower bound to the marginal likelihood. The objective automatically embodies an Occam's Razor effect that avoids collapse of conservation laws to the trivial constant, without the need to manually add and tune additional regularisers. We demonstrate a proof-ofprinciple on n-harmonic oscillators and n-body systems. We find that our method correctly identifies the correct conserved quantities and U(n) and SE(n) symmetry groups, improving overall performance and predictive accuracy on test data.

Simulation-based inference (SBI) is the preferred framework for estimating parameters of intractable models in science and engineering. A significant challenge in this context is the large computational cost of simulating data from complex models, and the fact that this cost often depends on parameter values. We therefore propose \textit{cost-aware SBI methods} which can significantly reduce the cost of existing sampling-based SBI methods, such as neural SBI and approximate Bayesian computation. This is achieved through a combination of rejection and self-normalised importance sampling, which significantly reduces the number of expensive simulations needed. Our approach is studied extensively on models from epidemiology to telecommunications engineering, where we obtain significant reductions in the overall cost of inference.

Virtually any model we use in machine learning to make predictions does not perfectly represent reality. So, most of the learning happens under model misspecification. In this work, we present a novel analysis of the generalization performance of Bayesian model averaging under model misspecification and i.i.d. This analysis shows, in simple and intuitive terms, that Bayesian model averaging provides suboptimal generalization performance when the model is misspecified. In consequence, we provide strong theoretical arguments showing that Bayesian methods are not optimal for learning predictive models, unless the model class is perfectly specified.

The log-likelihood of a generative model often involves both positive and negative terms. As a result, maximum likelihood estimation is expensive. We show how to instead apply a version of noise-contrastive estimation---a general parameter estimation method with a less expensive stochastic objective. Our specific instantiation of this general idea works out in an interestingly non-trivial way and has provable guarantees for its optimality, consistency and efficiency. On several synthetic and real-world datasets, our method shows benefits: for the model to achieve the same level of log-likelihood on held-out data, our method needs considerably fewer function evaluations and less wall-clock time.

Conventional imitation learning assumes access to the actions of demonstrators, but these motor signals are often non-observable in naturalistic settings. To address these challenges, we explore deep generative modeling of state-only sequences with non-Markov Decision Process (nMDP), where the policy is an energy-based prior in the latent space of the state transition generator. We develop maximum likelihood estimation to achieve model-based imitation, which involves short-run MCMC sampling from the prior and importance sampling for the posterior. The learned model enables \textit{decision-making as inference}: model-free policy execution is equivalent to prior sampling, model-based planning is posterior sampling initialized from the policy. We demonstrate the efficacy of the proposed method in a prototypical path planning task with non-Markovian constraints and show that the learned model exhibits strong performances in challenging domains from the MuJoCo suite.

Modern CNN-based object detectors assign anchors for ground-truth objects under the restriction of object-anchor Intersection-over-Unit (IoU). In this study, we propose a learning-to-match approach to break IoU restriction, allowing objects to match anchors in a flexible manner. Our approach, referred to as FreeAnchor, updates hand-crafted anchor assignment to "free" anchor matching by formulating detector training as a maximum likelihood estimation (MLE) procedure. FreeAnchor targets at learning features which best explain a class of objects in terms of both classification and localization. FreeAnchor is implemented by optimizing detection customized likelihood and can be fused with CNN-based detectors in a plug-and-play manner.

The key distinguishing property of a Bayesian approach is marginalization, rather than using a single setting of weights. Bayesian marginalization can particularly improve the accuracy and calibration of modern deep neural networks, which are typically underspecified by the data, and can represent many compelling but different solutions. We show that deep ensembles provide an effective mechanism for approximate Bayesian marginalization, and propose a related approach that further improves the predictive distribution by marginalizing within basins of attraction, without significant overhead. We also investigate the prior over functions implied by a vague distribution over neural network weights, explaining the generalization properties of such models from a probabilistic perspective. From this perspective, we explain results that have been presented as mysterious and distinct to neural network generalization, such as the ability to fit images with random labels, and show that these results can be reproduced with Gaussian processes.