Functional data describe a wide range of processes encountered in practice, such as growth curves and spectral absorption. Functional regression considers a version of regression, where both the response and covariates are functional data. Evaluating both the functional relatedness between the response and covariates and the relatedness of a multivariate response function can be challenging. In this paper, we propose a solution for both these issues, by means of a functional Gaussian graphical regression model. It extends the notion of conditional Gaussian graphical models to partially separable functions. For inference, we propose a double-penalized estimator. Additionally, we present a novel adaptation of Kullback-Leibler cross-validation tailored for graph estimators which accounts for precision and regression matrices when the population presents one or more sub-groups, named joint Kullback-Leibler cross-validation. Evaluation of model performance is done in terms of Kullback-Leibler divergence and graph recovery power. We illustrate the method on a air pollution dataset.
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Disentangled Representation Learning (DRL) aims to learn a model capable of identifying and disentangling the underlying factors hidden in the observable data in representation form. The process of separating underlying factors of variation into variables with semantic meaning benefits in learning explainable representations of data, which imitates the meaningful understanding process of humans when observing an object or relation. As a general learning strategy, DRL has demonstrated its power in improving the model explainability, controlability, robustness, as well as generalization capacity in a wide range of scenarios such as computer vision, natural language processing, and data mining. In this article, we comprehensively investigate DRL from various aspects including motivations, definitions, methodologies, evaluations, applications, and model designs. We first present two well-recognized definitions, i.e., Intuitive Definition and Group Theory Definition for disentangled representation learning. We further categorize the methodologies for DRL into four groups from the following perspectives, the model type, representation structure, supervision signal, and independence assumption. We also analyze principles to design different DRL models that may benefit different tasks in practical applications. Finally, we point out challenges in DRL as well as potential research directions deserving future investigations. We believe this work may provide insights for promoting the DRL research in the community.
Selective inference is the problem of giving valid answers to statistical questions chosen in a data-driven manner. A standard solution to selective inference is simultaneous inference, which delivers valid answers to the set of all questions that could possibly have been asked. However, simultaneous inference can be unnecessarily conservative if this set includes many questions that were unlikely to be asked in the first place. We introduce a less conservative solution to selective inference that we call locally simultaneous inference, which only answers those questions that could plausibly have been asked in light of the observed data, all the while preserving rigorous type I error guarantees. For example, if the objective is to construct a confidence interval for the "winning" treatment effect in a clinical trial with multiple treatments, and it is obvious in hindsight that only one treatment had a chance to win, then our approach will return an interval that is nearly the same as the uncorrected, standard interval. Locally simultaneous inference is implemented by refining any method for simultaneous inference of interest. Under mild conditions satisfied by common confidence intervals, locally simultaneous inference strictly dominates its underlying simultaneous inference method, meaning it can never yield less statistical power but only more. Compared to conditional selective inference, which demands stronger guarantees, locally simultaneous inference is more easily applicable in nonparametric settings and is more numerically stable.
Most existing temporal point process models are characterized by conditional intensity function. These models often require numerical approximation methods for likelihood evaluation, which potentially hurts their performance. By directly modelling the integral of the intensity function, i.e., the cumulative hazard function (CHF), the likelihood can be evaluated accurately, making it a promising approach. However, existing CHF-based methods are not well-defined, i.e., the mathematical constraints of CHF are not completely satisfied, leading to untrustworthy results. For multivariate temporal point process, most existing methods model intensity (or density, etc.) functions for each variate, limiting the scalability. In this paper, we explore using neural networks to model a flexible but well-defined CHF and learning the multivariate temporal point process with low parameter complexity. Experimental results on six datasets show that the proposed model achieves the state-of-the-art performance on data fitting and event prediction tasks while having significantly fewer parameters and memory usage than the strong competitors. The source code and data can be obtained from //github.com/lbq8942/NPP.
One of the most important processing steps in any analysis pipeline is handling missing data. Traditional approaches simply delete any sample or feature with missing elements. Recent imputation methods replace missing data based on assumed relationships between observed data and the missing elements. However, there is a largely under-explored alternative amid these extremes. Partial deletion approaches remove excessive amounts of missing data, as defined by the user. They can be used in place of traditional deletion or as a precursor to imputation. In this manuscript, we expand upon the Mr. Clean suite of algorithms, focusing on the scenario where all missing data is removed. We show that the RowCol Integer Program can be recast as a Linear Program, thereby reducing runtime. Additionally, the Element Integer Program can be reformulated to reduce the number of variables and allow for high levels of parallelization. Using real-world data sets from genetic, gene expression, and single cell RNA-seq experiments we demonstrate that our algorithms outperform existing deletion techniques over several missingness values, balancing runtime and data retention. Our combined greedy algorithm retains the maximum number of valid elements in 126 of 150 scenarios and stays within 1\% of maximum in 23 of the remaining experiments. The reformulated Element IP complements the greedy algorithm when removing all missing data, boasting a reduced runtime and increase in valid elements in larger data sets, over its generic counterpart. These two programs greatly increase the amount of valid data retained over traditional deletion techniques and further improve on existing partial deletion algorithms.
Rapid advances in designing cognitive and counter-adversarial systems have motivated the development of inverse Bayesian filters. In this setting, a cognitive 'adversary' tracks its target of interest via a stochastic framework such as a Kalman filter (KF). The target or 'defender' then employs another inverse stochastic filter to infer the forward filter estimates of the defender computed by the adversary. For linear systems, the inverse Kalman filter (I-KF) has been recently shown to be effective in these counter-adversarial applications. In the paper, contrary to prior works, we focus on non-linear system dynamics and formulate the inverse unscented KF (I-UKF) to estimate the defender's state based on the unscented transform, or equivalently, statistical linearization technique. We then generalize this framework to unknown systems by proposing reproducing kernel Hilbert space-based UKF (RKHS-UKF) to learn the system dynamics and estimate the state based on its observations. Our theoretical analyses to guarantee the stochastic stability of I-UKF and RKHS-UKF in the mean-squared sense show that, provided the forward filters are stable, the inverse filters are also stable under mild system-level conditions. We show that, despite being a suboptimal filter, our proposed I-UKF is a conservative estimator, i.e., I-UKF's estimated error covariance upper-bounds its true value. Our numerical experiments for several different applications demonstrate the estimation performance of the proposed filters using recursive Cram\'{e}r-Rao lower bound and non-credibility index (NCI).
Automated industries lead to high quality production, lower manufacturing cost and better utilization of human resources. Robotic manipulator arms have major role in the automation process. However, for complex manipulation tasks, hard coding efficient and safe trajectories is challenging and time consuming. Machine learning methods have the potential to learn such controllers based on expert demonstrations. Despite promising advances, better approaches must be developed to improve safety, reliability, and efficiency of ML methods in both training and deployment phases. This survey aims to review cutting edge technologies and recent trends on ML methods applied to real-world manipulation tasks. After reviewing the related background on ML, the rest of the paper is devoted to ML applications in different domains such as industry, healthcare, agriculture, space, military, and search and rescue. The paper is closed with important research directions for future works.
The conjoining of dynamical systems and deep learning has become a topic of great interest. In particular, neural differential equations (NDEs) demonstrate that neural networks and differential equation are two sides of the same coin. Traditional parameterised differential equations are a special case. Many popular neural network architectures, such as residual networks and recurrent networks, are discretisations. NDEs are suitable for tackling generative problems, dynamical systems, and time series (particularly in physics, finance, ...) and are thus of interest to both modern machine learning and traditional mathematical modelling. NDEs offer high-capacity function approximation, strong priors on model space, the ability to handle irregular data, memory efficiency, and a wealth of available theory on both sides. This doctoral thesis provides an in-depth survey of the field. Topics include: neural ordinary differential equations (e.g. for hybrid neural/mechanistic modelling of physical systems); neural controlled differential equations (e.g. for learning functions of irregular time series); and neural stochastic differential equations (e.g. to produce generative models capable of representing complex stochastic dynamics, or sampling from complex high-dimensional distributions). Further topics include: numerical methods for NDEs (e.g. reversible differential equations solvers, backpropagation through differential equations, Brownian reconstruction); symbolic regression for dynamical systems (e.g. via regularised evolution); and deep implicit models (e.g. deep equilibrium models, differentiable optimisation). We anticipate this thesis will be of interest to anyone interested in the marriage of deep learning with dynamical systems, and hope it will provide a useful reference for the current state of the art.
Graph Neural Networks (GNNs) draw their strength from explicitly modeling the topological information of structured data. However, existing GNNs suffer from limited capability in capturing the hierarchical graph representation which plays an important role in graph classification. In this paper, we innovatively propose hierarchical graph capsule network (HGCN) that can jointly learn node embeddings and extract graph hierarchies. Specifically, disentangled graph capsules are established by identifying heterogeneous factors underlying each node, such that their instantiation parameters represent different properties of the same entity. To learn the hierarchical representation, HGCN characterizes the part-whole relationship between lower-level capsules (part) and higher-level capsules (whole) by explicitly considering the structure information among the parts. Experimental studies demonstrate the effectiveness of HGCN and the contribution of each component.
Embedding models for deterministic Knowledge Graphs (KG) have been extensively studied, with the purpose of capturing latent semantic relations between entities and incorporating the structured knowledge into machine learning. However, there are many KGs that model uncertain knowledge, which typically model the inherent uncertainty of relations facts with a confidence score, and embedding such uncertain knowledge represents an unresolved challenge. The capturing of uncertain knowledge will benefit many knowledge-driven applications such as question answering and semantic search by providing more natural characterization of the knowledge. In this paper, we propose a novel uncertain KG embedding model UKGE, which aims to preserve both structural and uncertainty information of relation facts in the embedding space. Unlike previous models that characterize relation facts with binary classification techniques, UKGE learns embeddings according to the confidence scores of uncertain relation facts. To further enhance the precision of UKGE, we also introduce probabilistic soft logic to infer confidence scores for unseen relation facts during training. We propose and evaluate two variants of UKGE based on different learning objectives. Experiments are conducted on three real-world uncertain KGs via three tasks, i.e. confidence prediction, relation fact ranking, and relation fact classification. UKGE shows effectiveness in capturing uncertain knowledge by achieving promising results on these tasks, and consistently outperforms baselines on these tasks.
We investigate a lattice-structured LSTM model for Chinese NER, which encodes a sequence of input characters as well as all potential words that match a lexicon. Compared with character-based methods, our model explicitly leverages word and word sequence information. Compared with word-based methods, lattice LSTM does not suffer from segmentation errors. Gated recurrent cells allow our model to choose the most relevant characters and words from a sentence for better NER results. Experiments on various datasets show that lattice LSTM outperforms both word-based and character-based LSTM baselines, achieving the best results.
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