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 introduce and investigate matrix approximation by decomposition into a sum of radial basis function (RBF) components. An RBF component is a generalization of the outer product between a pair of vectors, where an RBF function replaces the scalar multiplication between individual vector elements. Even though the RBF functions are positive definite, the summation across components is not restricted to convex combinations and allows us to compute the decomposition for any real matrix that is not necessarily symmetric or positive definite. We formulate the problem of seeking such a decomposition as an optimization problem with a nonlinear and non-convex loss function. Several modern versions of the gradient descent method, including their scalable stochastic counterparts, are used to solve this problem. We provide extensive empirical evidence of the effectiveness of the RBF decomposition and that of the gradient-based fitting algorithm. While being conceptually motivated by singular value decomposition (SVD), our proposed nonlinear counterpart outperforms SVD by drastically reducing the memory required to approximate a data matrix with the same $L_2$-error for a wide range of matrix types. For example, it leads to 2 to 10 times memory save for Gaussian noise, graph adjacency matrices, and kernel matrices. Moreover, this proximity-based decomposition can offer additional interpretability in applications that involve, e.g., capturing the inner low-dimensional structure of the data, retaining graph connectivity structure, and preserving the acutance of images.

In this paper, we propose a gradient boosting algorithm for large-scale regression problems called \textit{Gradient Boosted Binary Histogram Ensemble} (GBBHE) based on binary histogram partition and ensemble learning. From the theoretical perspective, by assuming the H\"{o}lder continuity of the target function, we establish the statistical convergence rate of GBBHE in the space $C^{0,\alpha}$ and $C^{1,0}$, where a lower bound of the convergence rate for the base learner demonstrates the advantage of boosting. Moreover, in the space $C^{1,0}$, we prove that the number of iterations to achieve the fast convergence rate can be reduced by using ensemble regressor as the base learner, which improves the computational efficiency. In the experiments, compared with other state-of-the-art algorithms such as gradient boosted regression tree (GBRT), Breiman's forest, and kernel-based methods, our GBBHE algorithm shows promising performance with less running time on large-scale datasets.

We derive a Matern Gaussian process (GP) on the vertices of a hypergraph. This enables estimation of regression models of observed or latent values associated with the vertices, in which the correlation and uncertainty estimates are informed by the hypergraph structure. We further present a framework for embedding the vertices of a hypergraph into a latent space using the hypergraph GP. Finally, we provide a scheme for identifying a small number of representative inducing vertices that enables scalable inference through sparse GPs. We demonstrate the utility of our framework on three challenging real-world problems that concern multi-class classification for the political party affiliation of legislators on the basis of voting behaviour, probabilistic matrix factorisation of movie reviews, and embedding a hypergraph of animals into a low-dimensional latent space.

We address the estimation of conditional average treatment effects (CATEs) when treatments are graph-structured (e.g., molecular graphs of drugs). Given a weak condition on the effect, we propose a plug-in estimator that decomposes CATE estimation into separate, simpler optimization problems. Our estimator (a) isolates the causal estimands (reducing regularization bias), and (b) allows one to plug in arbitrary models for learning. In experiments with small-world and molecular graphs, we show that our approach outperforms prior approaches and is robust to varying selection biases.

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.

Empirical risk minimization (ERM) is the workhorse of machine learning, whether for classification and regression or for off-policy policy learning, but its model-agnostic guarantees can fail when we use adaptively collected data, such as the result of running a contextual bandit algorithm. We study a generic importance sampling weighted ERM algorithm for using adaptively collected data to minimize the average of a loss function over a hypothesis class and provide first-of-their-kind generalization guarantees and fast convergence rates. Our results are based on a new maximal inequality that carefully leverages the importance sampling structure to obtain rates with the right dependence on the exploration rate in the data. For regression, we provide fast rates that leverage the strong convexity of squared-error loss. For policy learning, we provide rate-optimal regret guarantees that close an open gap in the existing literature whenever exploration decays to zero, as is the case for bandit-collected data. An empirical investigation validates our theory.

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.

In this new series, I took it upon myself to improve my coding skills and habits by writing clean, reusable, well-documented code with test cases. This is the first part of the series where I implement Linear, Polynomial, Ridge, Lasso, and ElasticNet Regression from scratch in an object-oriented manner. We'll start with a simple LinearRegression class and then build upon it creating an entire module of linear models in a simple style similar to Scikit-Learn. My implementations are in no way optimal solutions and are only meant to increase our understanding of machine learning. In the repository you will find all of the code found in this blog and more including test cases for every class and function.