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Physically-inspired latent force models offer an interpretable alternative to purely data driven tools for inference in dynamical systems. They carry the structure of differential equations and the flexibility of Gaussian processes, yielding interpretable parameters and dynamics-imposed latent functions. However, the existing inference techniques associated with these models rely on the exact computation of posterior kernel terms which are seldom available in analytical form. Most applications relevant to practitioners, such as Hill equations or diffusion equations, are hence intractable. In this paper, we overcome these computational problems by proposing a variational solution to a general class of non-linear and parabolic partial differential equation latent force models. Further, we show that a neural operator approach can scale our model to thousands of instances, enabling fast, distributed computation. We demonstrate the efficacy and flexibility of our framework by achieving competitive performance on several tasks where the kernels are of varying degrees of tractability.

We propose Streaming Bandits, a Restless Multi Armed Bandit (RMAB) framework in which heterogeneous arms may arrive and leave the system after staying on for a finite lifetime. Streaming Bandits naturally capture the health intervention planning problem, where health workers must manage the health outcomes of a patient cohort while new patients join and existing patients leave the cohort each day. Our contributions are as follows: (1) We derive conditions under which our problem satisfies indexability, a precondition that guarantees the existence and asymptotic optimality of the Whittle Index solution for RMABs. We establish the conditions using a polytime reduction of the Streaming Bandit setup to regular RMABs. (2) We further prove a phenomenon that we call index decay, whereby the Whittle index values are low for short residual lifetimes driving the intuition underpinning our algorithm. (3) We propose a novel and efficient algorithm to compute the index-based solution for Streaming Bandits. Unlike previous methods, our algorithm does not rely on solving the costly finite horizon problem on each arm of the RMAB, thereby lowering the computational complexity compared to existing methods. (4) Finally, we evaluate our approach via simulations run on realworld data sets from a tuberculosis patient monitoring task and an intervention planning task for improving maternal healthcare, in addition to other synthetic domains. Across the board, our algorithm achieves a 2-orders-of-magnitude speed-up over existing methods while maintaining the same solution quality.

The recursive and hierarchical structure of full rooted trees is applicable to represent statistical models in various areas, such as data compression, image processing, and machine learning. In most of these cases, the full rooted tree is not a random variable; as such, model selection to avoid overfitting becomes problematic. A method to solve this problem is to assume a prior distribution on the full rooted trees. This enables the optimal model selection based on the Bayes decision theory. For example, by assigning a low prior probability to a complex model, the maximum a posteriori estimator prevents the selection of the complex one. Furthermore, we can average all the models weighted by their posteriors. In this paper, we propose a probability distribution on a set of full rooted trees. Its parametric representation is suitable for calculating the properties of our distribution using recursive functions, such as the mode, expectation, and posterior distribution. Although such distributions have been proposed in previous studies, they are only applicable to specific applications. Therefore, we extract their mathematically essential components and derive new generalized methods to calculate the expectation, posterior distribution, etc.

A determinantal point process (DPP) on a collection of $M$ items is a model, parameterized by a symmetric kernel matrix, that assigns a probability to every subset of those items. Recent work shows that removing the kernel symmetry constraint, yielding nonsymmetric DPPs (NDPPs), can lead to significant predictive performance gains for machine learning applications. However, existing work leaves open the question of scalable NDPP sampling. There is only one known DPP sampling algorithm, based on Cholesky decomposition, that can directly apply to NDPPs as well. Unfortunately, its runtime is cubic in $M$, and thus does not scale to large item collections. In this work, we first note that this algorithm can be transformed into a linear-time one for kernels with low-rank structure. Furthermore, we develop a scalable sublinear-time rejection sampling algorithm by constructing a novel proposal distribution. Additionally, we show that imposing certain structural constraints on the NDPP kernel enables us to bound the rejection rate in a way that depends only on the kernel rank. In our experiments we compare the speed of all of these samplers for a variety of real-world tasks.

Software technology has high impact on the global economy as in many sectors of contemporary society. As a product enabling the most varied daily activities, the software product has to be produced reflecting high quality. Software quality is dependent on its development that is based in a large set of software development processes. However, the implementation and continuous improvement of software process aimed at software product should be carefully institutionalized by software development organizations such as software factories, testing factories, V&V organizations, among others. The institutionalization of programs such as a Software Process Improvement Program, or SPI Program, require a strategic planning, which is addressed in this article from the perspective of specific models and frameworks, as well as reflections based on software process engineering models and standards. In addition, a set of strategic drivers is proposed to assist the implementation of a Strategic Plan for a SPI Program which can be considered by the organizations before starting this kind of Program.

Learning a graph topology to reveal the underlying relationship between data entities plays an important role in various machine learning and data analysis tasks. Under the assumption that structured data vary smoothly over a graph, the problem can be formulated as a regularised convex optimisation over a positive semidefinite cone and solved by iterative algorithms. Classic methods require an explicit convex function to reflect generic topological priors, e.g. the $\ell_1$ penalty for enforcing sparsity, which limits the flexibility and expressiveness in learning rich topological structures. We propose to learn a mapping from node data to the graph structure based on the idea of learning to optimise (L2O). Specifically, our model first unrolls an iterative primal-dual splitting algorithm into a neural network. The key structural proximal projection is replaced with a variational autoencoder that refines the estimated graph with enhanced topological properties. The model is trained in an end-to-end fashion with pairs of node data and graph samples. Experiments on both synthetic and real-world data demonstrate that our model is more efficient than classic iterative algorithms in learning a graph with specific topological properties.

Spatio-temporal forecasting has numerous applications in analyzing wireless, traffic, and financial networks. Many classical statistical models often fall short in handling the complexity and high non-linearity present in time-series data. Recent advances in deep learning allow for better modelling of spatial and temporal dependencies. While most of these models focus on obtaining accurate point forecasts, they do not characterize the prediction uncertainty. In this work, we consider the time-series data as a random realization from a nonlinear state-space model and target Bayesian inference of the hidden states for probabilistic forecasting. We use particle flow as the tool for approximating the posterior distribution of the states, as it is shown to be highly effective in complex, high-dimensional settings. Thorough experimentation on several real world time-series datasets demonstrates that our approach provides better characterization of uncertainty while maintaining comparable accuracy to the state-of-the art point forecasting methods.

Markov Logic Networks (MLNs), which elegantly combine logic rules and probabilistic graphical models, can be used to address many knowledge graph problems. However, inference in MLN is computationally intensive, making the industrial-scale application of MLN very difficult. In recent years, graph neural networks (GNNs) have emerged as efficient and effective tools for large-scale graph problems. Nevertheless, GNNs do not explicitly incorporate prior logic rules into the models, and may require many labeled examples for a target task. In this paper, we explore the combination of MLNs and GNNs, and use graph neural networks for variational inference in MLN. We propose a GNN variant, named ExpressGNN, which strikes a nice balance between the representation power and the simplicity of the model. Our extensive experiments on several benchmark datasets demonstrate that ExpressGNN leads to effective and efficient probabilistic logic reasoning.

A fundamental computation for statistical inference and accurate decision-making is to compute the marginal probabilities or most probable states of task-relevant variables. Probabilistic graphical models can efficiently represent the structure of such complex data, but performing these inferences is generally difficult. Message-passing algorithms, such as belief propagation, are a natural way to disseminate evidence amongst correlated variables while exploiting the graph structure, but these algorithms can struggle when the conditional dependency graphs contain loops. Here we use Graph Neural Networks (GNNs) to learn a message-passing algorithm that solves these inference tasks. We first show that the architecture of GNNs is well-matched to inference tasks. We then demonstrate the efficacy of this inference approach by training GNNs on a collection of graphical models and showing that they substantially outperform belief propagation on loopy graphs. Our message-passing algorithms generalize out of the training set to larger graphs and graphs with different structure.

Probabilistic topic models are popular unsupervised learning methods, including probabilistic latent semantic indexing (pLSI) and latent Dirichlet allocation (LDA). By now, their training is implemented on general purpose computers (GPCs), which are flexible in programming but energy-consuming. Towards low-energy implementations, this paper investigates their training on an emerging hardware technology called the neuromorphic multi-chip systems (NMSs). NMSs are very effective for a family of algorithms called spiking neural networks (SNNs). We present three SNNs to train topic models. The first SNN is a batch algorithm combining the conventional collapsed Gibbs sampling (CGS) algorithm and an inference SNN to train LDA. The other two SNNs are online algorithms targeting at both energy- and storage-limited environments. The two online algorithms are equivalent with training LDA by using maximum-a-posterior estimation and maximizing the semi-collapsed likelihood, respectively. They use novel, tailored ordinary differential equations for stochastic optimization. We simulate the new algorithms and show that they are comparable with the GPC algorithms, while being suitable for NMS implementation. We also propose an extension to train pLSI and a method to prune the network to obey the limited fan-in of some NMSs.