Incomplete instances with various missing attributes in many real-world scenes have brought challenges to the classification task. There are some missing values imputation methods to fill the missing values with substitute values before classification. However, the separation between imputation and classification may lead to inferior performance since label information are ignored during imputation. Moreover, these imputation methods tend to initialize these missing values with strong prior assumptions, while the unreliability of such initialization is rarely considered. To tackle these problems, a novel semi-supervised conditional normalizing flow (SSCFlow) is proposed in this paper. SSCFlow explicitly utilizes the observed labels to facilitate the imputation and classification simultaneously by employing a semi-supervised algorithm to estimate the conditional probability density of missing values. Moreover, SSCFlow takes the initialized missing values as corrupted initial imputation and iteratively reconstructs their latent representations with an overcomplete denoising autoencoder to approximate the true conditional probability density of missing values. Experiments have been conducted with real-world datasets to demonstrate the robustness and efficiency of the proposed algorithm.

Design-by-Analogy (DbA) is a design methodology, wherein new solutions are generated in a target domain based on inspiration drawn from a source domain through cross-domain analogical reasoning [1, 2, 3]. DbA is an active research area in engineering design and various methods and tools have been proposed to support the implement of its process [4, 5, 6, 7, 8]. Studies have shown that DbA can help designers mitigate design fixation [9] and improve design ideation outcomes [10]. Fig.1 presents an example of DbA applications [11]. This case aims to solve an engineering design problem: How might we rectify the loud sonic boom generated when trains travel at high speeds through tunnels in atmospheric conditions [11, 12]? For potential design solutions to this problem, engineers explored structures in other design fields than trains or in the nature that effectively "break" the sonic-boom effect. When looking into the nature, engineers discovered that kingfisher birds could slice through the air and dive into the water at extremely high speeds to catch prey while barely making a splash. By analogy, engineers re-designed the train's front-end nose to mimic the geometry of the kingfisher's beak. This analogical design reduced noise and eliminated tunnel booms.

We use the theory of normal variance-mean mixtures to derive a data augmentation scheme for models that include gamma functions. Our methodology applies to many situations in statistics and machine learning, including Multinomial-Dirichlet distributions, Negative binomial regression, Poisson-Gamma hierarchical models, Extreme value models, to name but a few. All of those models include a gamma function which does not admit a natural conjugate prior distribution providing a significant challenge to inference and prediction. To provide a data augmentation strategy, we construct and develop the theory of the class of Exponential Reciprocal Gamma distributions. This allows scalable EM and MCMC algorithms to be developed. We illustrate our methodology on a number of examples, including gamma shape inference, negative binomial regression and Dirichlet allocation. Finally, we conclude with directions for future research.

Simulation-based inference enables learning the parameters of a model even when its likelihood cannot be computed in practice. One class of methods uses data simulated with different parameters to infer an amortized estimator for the likelihood-to-evidence ratio, or equivalently the posterior function. We show that this approach can be formulated in terms of mutual information maximization between model parameters and simulated data. We use this equivalence to reinterpret existing approaches for amortized inference, and propose two new methods that rely on lower bounds of the mutual information. We apply our framework to the inference of parameters of stochastic processes and chaotic dynamical systems from sampled trajectories, using artificial neural networks for posterior prediction. Our approach provides a unified framework that leverages the power of mutual information estimators for inference.

Combining the outputs of multiple classifiers or experts into a single probabilistic classification is a fundamental task in machine learning with broad applications from classifier fusion to expert opinion pooling. Here we present a hierarchical Bayesian model of probabilistic classifier fusion based on a new correlated Dirichlet distribution. This distribution explicitly models positive correlations between marginally Dirichlet-distributed random vectors thereby allowing normative modeling of correlations between base classifiers or experts. The proposed model naturally accommodates the classic Independent Opinion Pool and other independent fusion algorithms as special cases. It is evaluated by uncertainty reduction and correctness of fusion on synthetic and real-world data sets. We show that a change in performance of the fused classifier due to uncertainty reduction can be Bayes optimal even for highly correlated base classifiers.

Active learning methods have recently surged in the literature due to their ability to solve complex structural reliability problems within an affordable computational cost. These methods are designed by adaptively building an inexpensive surrogate of the original limit-state function. Examples of such surrogates include Gaussian process models which have been adopted in many contributions, the most popular ones being the efficient global reliability analysis (EGRA) and the active Kriging Monte Carlo simulation (AK-MCS), two milestone contributions in the field. In this paper, we first conduct a survey of the recent literature, showing that most of the proposed methods actually span from modifying one or more aspects of the two aforementioned methods. We then propose a generalized modular framework to build on-the-fly efficient active learning strategies by combining the following four ingredients or modules: surrogate model, reliability estimation algorithm, learning function and stopping criterion. Using this framework, we devise 39 strategies for the solution of 20 reliability benchmark problems. The results of this extensive benchmark are analyzed under various criteria leading to a synthesized set of recommendations for practitioners. These may be refined with a priori knowledge about the feature of the problem to solve, i.e., dimensionality and magnitude of the failure probability. This benchmark has eventually highlighted the importance of using surrogates in conjunction with sophisticated reliability estimation algorithms as a way to enhance the efficiency of the latter.

It was the event that "initiated AI as a research discipline," which grew to encompass multiple approaches, from the symbolic AI of the 1950s and 1960s to the statistical analysis and machine learning of the 1970s and 1980s to today's deep learning, the statistical analysis of "big data." But the preoccupation with developing practical methods for making machines behave as if they were humans emerged already 7 centuries ago. By using this "Contrivance," "the most ignorant Person at a reasonable Charge, and with a little bodily Labour, may write Books in Philosophy, Poetry, Politicks, Law, Mathematicks, and Theology, with the least Assistance from Genius or study." Bayesian inference will become a leading approach in machine learning. The boat was equipped with, as Tesla described it, "a borrowed mind."

Heterogeneous computing systems provide high performance and energy efficiency. However, to optimally utilize such systems, solutions that distribute the work across host CPUs and accelerating devices are needed. In this paper, we present a performance and energy aware approach that combines AI planning heuristics for parameter space exploration with a machine learning model for performance and energy evaluation to determine a near-optimal system configuration. For data-parallel applications our approach determines a near-optimal host-device distribution of work, number of processing units required and the corresponding scheduling strategy. We evaluate our approach for various heterogeneous systems accelerated with GPU or the Intel Xeon Phi. The experimental results demonstrate that our approach finds a near-optimal system configuration by evaluating only about 7% of reasonable configurations. Furthermore, the performance per Joule estimation of system configurations using our machine learning model is more than 1000x faster compared to the system evaluation by program execution.

In recent years, causal modelling has been used widely to improve generalization and to provide interpretability in machine learning models. To determine cause-effect relationships in the absence of a randomized trial, we can model causal systems with counterfactuals and interventions given enough domain knowledge. However, there are several cases where domain knowledge is almost absent and the only recourse is using a statistical method to estimate causal relationships. While there have been several works done in estimating causal relationships in unstructured data, we are yet to find a well-defined framework for estimating causal relationships in Knowledge Graphs (KG). It is commonly used to provide a semantic framework for data with complex inter-domain relationships. In this work, we define a hybrid approach that allows us to discover cause-effect relationships in KG. The proposed approach is based around the finding of the instantaneous causal structure of a non-experimental matrix using a non-Gaussian model, i.e; finding the causal ordering of the variables in a non-Gaussian setting. The non-experimental matrix is a low-dimensional tensor projection obtained by decomposing the adjacency tensor of a KG. We use two different pre-existing algorithms, one for the causal discovery and the other for decomposing the KG and combining them to get the causal structure in a KG.

Normalizing Flows (NFs) are universal density estimators based on Neuronal Networks. However, this universality is limited: the density's support needs to be diffeomorphic to a Euclidean space. In this paper, we propose a novel method to overcome this limitation without sacrificing universality. The proposed method inflates the data manifold by adding noise in the normal space, trains an NF on this inflated manifold, and, finally, deflates the learned density. Our main result provides sufficient conditions on the manifold and the specific choice of noise under which the corresponding estimator is exact. Our method has the same computational complexity as NFs and does not require computing an inverse flow. We also show that, if the embedding dimension is much larger than the manifold dimension, noise in the normal space can be well approximated by Gaussian noise. This allows to use our method for approximating arbitrary densities on non-flat manifolds provided that the manifold dimension is known.