The use of optimal transport cost for learning generative models has become popular with Wasserstein Generative Adversarial Networks (WGAN). Training of WGAN relies on a theoretical background: the calculation of the gradient of the optimal transport cost with respect to the generative model parameters. We first demonstrate that such gradient may not be defined, which can result in numerical instabilities during gradient-based optimization. We address this issue by stating a valid differentiation theorem in the case of entropic regularized transport and specify conditions under which existence is ensured. By exploiting the discrete nature of empirical data, we formulate the gradient in a semi-discrete setting and propose an algorithm for the optimization of the generative model parameters. Finally, we illustrate numerically the advantage of the proposed framework.
This paper investigates the problem of online statistical inference of model parameters in stochastic optimization problems via the Kiefer-Wolfowitz algorithm with random search directions. We first present the asymptotic distribution for the Polyak-Ruppert-averaging type Kiefer-Wolfowitz (AKW) estimators, whose asymptotic covariance matrices depend on the distribution of search directions and the function-value query complexity. The distributional result reflects the trade-off between statistical efficiency and function query complexity. We further analyze the choice of random search directions to minimize certain summary statistics of the asymptotic covariance matrix. Based on the asymptotic distribution, we conduct online statistical inference by providing two construction procedures of valid confidence intervals.
How to effectively and efficiently extract valid and reliable features from high-dimensional electroencephalography (EEG), particularly how to fuse the spatial and temporal dynamic brain information into a better feature representation, is a critical issue in brain data analysis. Most current EEG studies work in a task driven manner and explore the valid EEG features with a supervised model, which would be limited by the given labels to a great extent. In this paper, we propose a practical hybrid unsupervised deep convolutional recurrent generative adversarial network based EEG feature characterization and fusion model, which is termed as EEGFuseNet. EEGFuseNet is trained in an unsupervised manner, and deep EEG features covering both spatial and temporal dynamics are automatically characterized. Comparing to the existing features, the characterized deep EEG features could be considered to be more generic and independent of any specific EEG task. The performance of the extracted deep and low-dimensional features by EEGFuseNet is carefully evaluated in an unsupervised emotion recognition application based on three public emotion databases. The results demonstrate the proposed EEGFuseNet is a robust and reliable model, which is easy to train and performs efficiently in the representation and fusion of dynamic EEG features. In particular, EEGFuseNet is established as an optimal unsupervised fusion model with promising cross-subject emotion recognition performance. It proves EEGFuseNet is capable of characterizing and fusing deep features that imply comparative cortical dynamic significance corresponding to the changing of different emotion states, and also demonstrates the possibility of realizing EEG based cross-subject emotion recognition in a pure unsupervised manner.
Modern mathematics is built on the idea that proofs should be translatable into formal proofs, whose validity is an objective question, decidable by a computer. Yet, in practice, proofs are informal and may omit many details. An agent considers a proof valid if they trust that it could be expanded into a machine-verifiable proof. A proof's validity can thus become a subjective matter and lead to a debate, which may be difficult to settle. Hence, while the concept of valid proof is well-defined, the process to establish validity is itself a complex multi-agent problem. We introduce the SPRIG protocol. SPRIG allows agents to propose and verify succinct and informative proofs in a decentralized fashion; the trust is established by agents being able to request more details in the proof steps; debates, if they arise, must isolate details of proofs and, if they persist, go down to machine-level details, where they are automatically settled. A structure of bounties and stakes is set to incentivize agents to act in good faith. We propose a game-theoretic discussion of SPRIG, showing how agents with various types of information interact, leading to a proof tree with an appropriate level of detail and to the invalidation of wrong proofs, and we discuss resilience against various attacks. We then analyze a simplified model, characterize its equilibria and compute the agents' level of trust. SPRIG is designed to run as a smart contract on a blockchain platform. This allows anonymous agents to participate in the verification debate, and to contribute with their information. The smart contract mediates the interactions, settles debates, and guarantees that bounties and stakes are paid as specified. SPRIG enables new applications, such as the issuance of bounties for open problems, and the creation of derivatives markets, allowing agents to inject more information pertaining to proofs.
We present the ARC-DA dataset, a direct-answer ("open response", "freeform") version of the ARC (AI2 Reasoning Challenge) multiple-choice dataset. While ARC has been influential in the community, its multiple-choice format is unrepresentative of real-world questions, and multiple choice formats can be particularly susceptible to artifacts. The ARC-DA dataset addresses these concerns by converting questions to direct-answer format using a combination of crowdsourcing and expert review. The resulting dataset contains 2985 questions with a total of 8436 valid answers (questions typically have more than one valid answer). ARC-DA is one of the first DA datasets of natural questions that often require reasoning, and where appropriate question decompositions are not evident from the questions themselves. We describe the conversion approach taken, appropriate evaluation metrics, and several strong models. Although high, the best scores (81% GENIE, 61.4% F1, 63.2% ROUGE-L) still leave considerable room for improvement. In addition, the dataset provides a natural setting for new research on explanation, as many questions require reasoning to construct answers. We hope the dataset spurs further advances in complex question-answering by the community. ARC-DA is available at https://allenai.org/data/arc-da
The problem of finding an ancestral acyclic directed mixed graph (ADMG) that represents the causal relationships between a set of variables is an important area of research on causal inference. Most existing score-based structure learning methods focus on learning directed acyclic graph (DAG) models without latent variables. A number of score-based methods have recently been proposed for the ADMG learning, yet they are heuristic in nature and do not guarantee an optimal solution. We propose a novel exact score-based method that solves an integer programming (IP) formulation and returns a score-maximizing ancestral ADMG for a set of continuous variables that follow a multivariate Gaussian distribution. We generalize the state-of-the-art IP model for DAG learning problems and derive new classes of valid inequalities to formulate an IP model for ADMG learning. Empirically, our model can be solved efficiently for medium-sized problems and achieves better accuracy than state-of-the-art score-based methods as well as benchmark constraint-based methods.
In recent years, we have witnessed a surge of interests in learning a suitable distance metric from weakly supervised data. Most existing methods aim to pull all the similar samples closer while push the dissimilar ones as far as possible. However, when some classes of the dataset exhibit multimodal distribution, these goals conflict and thus can hardly be concurrently satisfied. Additionally, to ensure a valid metric, many methods require a repeated eigenvalue decomposition process, which is expensive and numerically unstable. Therefore, how to learn an appropriate distance metric from weakly supervised data remains an open but challenging problem. To address this issue, in this paper, we propose a novel weakly supervised metric learning algorithm, named MultimoDal Aware weakly supervised Metric Learning (MDaML). MDaML partitions the data space into several clusters and allocates the local cluster centers and weight for each sample. Then, combining it with the weighted triplet loss can further enhance the local separability, which encourages the local dissimilar samples to keep a large distance from the local similar samples. Meanwhile, MDaML casts the metric learning problem into an unconstrained optimization on the SPD manifold, which can be efficiently solved by Riemannian Conjugate Gradient Descent (RCGD). Extensive experiments conducted on 13 datasets validate the superiority of the proposed MDaML.
We consider the problem of inference in Difference-in-Differences (DID) when there are few treated units and errors are spatially correlated. We first show that, when there is a single treated unit, some existing inference methods designed for settings with few treated and many control units remain asymptotically valid when errors are weakly dependent. However, these methods may be invalid with more than one treated unit. We propose alternatives that are asymptotically valid in this setting, even when the relevant distance metric across units is unavailable.
Gas-liquid two-phase flow is a typical flow, and bubble characteristic measurement is of great importance to study the flow mechanism and guide the practical fluid mechanical engineering. In this paper, a novel three dimensional (3D) multiphase flow imaging device was designed to measure the transparent object that has an opaque object in the center of the observed area. Its mathematical model was built and the constraints were defined based on the geometrical relationship and design requirements. A modified harmony search (HS) algorithm was integrated and applied to optimize the arrangement of the single-camera-multi-mirror device. As a case study, the 3D multiphase flow imaging method was applied in the the 3D reconstruction of the cavitation bubble cluster inside a water hydraulic valve. The statistics of the Pareto data shows the good performance of the modified HS algorithm. And the cavitation experimental results shows that the method is valid, and the cavitation bubble cluster can be reconstructed with quite high precision.
Deep learning-based image inpainting algorithms have shown great performance via powerful learned prior from the numerous external natural images. However, they show unpleasant results on the test image whose distribution is far from the that of training images because their models are biased toward the training images. In this paper, we propose a simple image inpainting algorithm with test-time adaptation named AdaFill. Given a single out-of-distributed test image, our goal is to complete hole region more naturally than the pre-trained inpainting models. To achieve this goal, we treat remained valid regions of the test image as another training cues because natural images have strong internal similarities. From this test-time adaptation, our network can exploit externally learned image priors from the pre-trained features as well as the internal prior of the test image explicitly. Experimental results show that AdaFill outperforms other models on the various out-of-distribution test images. Furthermore, the model named ZeroFill, that are not pre-trained also sometimes outperforms the pre-trained models.
The discovery of Partial Differential Equations (PDEs) is an essential task for applied science and engineering. However, data-driven discovery of PDEs is generally challenging, primarily stemming from the sensitivity of the discovered equation to noise and the complexities of model selection. In this work, we propose an advanced Bayesian sparse learning algorithm for PDE discovery with variable coefficients, predominantly when the coefficients are spatially or temporally dependent. Specifically, we apply threshold Bayesian group Lasso regression with a spike-and-slab prior (tBGL-SS) and leverage a Gibbs sampler for Bayesian posterior estimation of PDE coefficients. This approach not only enhances the robustness of point estimation with valid uncertainty quantification but also relaxes the computational burden from Bayesian inference through the integration of coefficient thresholds as an approximate MCMC method. Moreover, from the quantified uncertainties, we propose a Bayesian total error bar criteria for model selection, which outperforms classic metrics including the root mean square and the Akaike information criterion. The capability of this method is illustrated by the discovery of several classical benchmark PDEs with spatially or temporally varying coefficients from solution data obtained from the reference simulations. In the experiments, we show that the tBGL-SS method is more robust than the baseline methods under noisy environments and provides better model selection criteria along the regularization path.
In online advertising, recommender systems try to propose items from a list of products to potential customers according to their interests. Such systems have been increasingly deployed in E-commerce due to the rapid growth of information technology and availability of large datasets. The ever-increasing progress in the field of artificial intelligence has provided powerful tools for dealing with such real-life problems. Deep reinforcement learning (RL) that deploys deep neural networks as universal function approximators can be viewed as a valid approach for design and implementation of recommender systems. This paper provides a comparative study between value-based and policy-based deep RL algorithms for designing recommender systems for online advertising. The RecoGym environment is adopted for training these RL-based recommender systems, where the long short term memory (LSTM) is deployed to build value and policy networks in these two approaches, respectively. LSTM is used to take account of the key role that order plays in the sequence of item observations by users. The designed recommender systems aim at maximising the click-through rate (CTR) for the recommended items. Finally, guidelines are provided for choosing proper RL algorithms for different scenarios that the recommender system is expected to handle.
We introduce a general framework of stochastic online convex optimization to obtain fast-rate stochastic regret bounds. We prove that algorithms such as online newton steps and a scale-free 10 version of Bernstein online aggregation achieve best-known rates in unbounded stochastic settings. We apply our approach to calibrate parametric probabilistic forecasters of non-stationary sub-gaussian time series. Our fast-rate stochastic regret bounds are any-time valid. Our proofs combine self-bounded and Poissonnian inequalities for martingales and sub-gaussian random variables, respectively, under a stochastic exp-concavity assumption.
Commonsense knowledge has proven to be beneficial to a variety of application areas, including question answering and natural language understanding. Previous work explored collecting commonsense knowledge triples automatically from text to increase the coverage of current commonsense knowledge graphs. We investigate a few machine learning approaches to mining commonsense knowledge triples using dictionary term definitions as inputs and provide some initial evaluation of the results. We start from extracting candidate triples using part-of-speech tag patterns from text, and then compare the performance of three existing models for triple scoring. Our experiments show that term definitions contain some valid and novel commonsense knowledge triples for some semantic relations, and also indicate some challenges with using existing triple scoring models.
There are relatively few works dealing with conformal prediction for multi-task learning issues, and this is particularly true for multi-target regression. This paper focuses on the problem of providing valid (i.e., frequency calibrated) multi-variate predictions. To do so, we propose to use copula functions applied to deep neural networks for inductive conformal prediction. We show that the proposed method ensures efficiency and validity for multi-target regression problems on various data sets.
We propose the task of disambiguating symbolic expressions in informal STEM documents in the form of LaTeX files - that is, determining their precise semantics and abstract syntax tree - as a neural machine translation task. We discuss the distinct challenges involved and present a dataset with roughly 33,000 entries. We evaluated several baseline models on this dataset, which failed to yield even syntactically valid LaTeX before overfitting. Consequently, we describe a methodology using a transformer language model pre-trained on sources obtained from arxiv.org, which yields promising results despite the small size of the dataset. We evaluate our model using a plurality of dedicated techniques, taking the syntax and semantics of symbolic expressions into account.
This paper presents a fully automatic approach to the scansion of Classical Greek hexameter verse. In particular, the paper describes an algorithm that uses deterministic finite-state automata and local linguistic rules to implement a targeted search for valid spondeus patterns and, in addition, a weighted finite-state transducer to correct and complete partial analyses and to reject invalid candidates. The paper also details the results of an empirical evaluation of the annotation quality resulting from this approach on hand-annotated data. It is shown that a finite-state approach provides quick and linguistically sound analyses of hexameter verses as well as an efficient formalisation of linguistic knowledge. The project code is available (see https://github.com/anetschka/greek_scansion).
DIHARD III was the third in a series of speaker diarization challenges intended to improve the robustness of diarization systems to variability in recording equipment, noise conditions, and conversational domain. Speaker diarization was evaluated under two speech activity conditions (diarization from a reference speech activity vs. diarization from scratch) and 11 diverse domains. The domains span a range of recording conditions and interaction types, including read audio-books, meeting speech, clinical interviews, web videos, and, for the first time, conversational telephone speech. A total of 30 organizations (forming 21teams) from industry and academia submitted 499 valid system outputs. The evaluation results indicate that speaker diarization has improved markedly since DIHARD I, particularly for two-party interactions, but that for many domains (e.g., web video) the problem remains far from solved.
Counterfactual explanations provide a potentially significant solution to the Explainable AI (XAI) problem, but good, native counterfactuals have been shown to rarely occur in most datasets. Hence, the most popular methods generate synthetic counterfactuals using blind perturbation. However, such methods have several shortcomings: the resulting counterfactuals (i) may not be valid data-points (they often use features that do not naturally occur), (ii) may lack the sparsity of good counterfactuals (if they modify too many features), and (iii) may lack diversity (if the generated counterfactuals are minimal variants of one another). We describe a method designed to overcome these problems, one that adapts native counterfactuals in the original dataset, to generate sparse, diverse synthetic counterfactuals from naturally occurring features. A series of experiments are reported that systematically explore parametric variations of this novel method on common datasets to establish the conditions for optimal performance.
This thesis is a proof of concept for the potential of Variational Auto-Encoder (VAE) on representation learning of real-world Knowledge Graphs (KG). Inspired by successful approaches to the generation of molecular graphs, we evaluate the capabilities of our model, the Relational Graph Variational Auto-Encoder (RGVAE). The impact of the modular hyperparameter choices, encoding through graph convolutions, graph matching and latent space prior, is compared. The RGVAE is first evaluated on link prediction. The mean reciprocal rank (MRR) scores on the two datasets FB15K-237 and WN18RR are compared to the embedding-based model DistMult. A variational DistMult and a RGVAE without latent space prior constraint are implemented as control models. The results show that between different settings, the RGVAE with relaxed latent space, scores highest on both datasets, yet does not outperform the DistMult. Further, we investigate the latent space in a twofold experiment: first, linear interpolation between the latent representation of two triples, then the exploration of each latent dimension in a $95\%$ confidence interval. Both interpolations show that the RGVAE learns to reconstruct the adjacency matrix but fails to disentangle. For the last experiment we introduce a new validation method for the FB15K-237 data set. The relation type-constrains of generated triples are filtered and matched with entity types. The observed rate of valid generated triples is insignificantly higher than the random threshold. All generated and valid triples are unseen. A comparison between different latent space priors, using the $\delta$-VAE method, reveals a decoder collapse. Finally we analyze the limiting factors of our approach compared to molecule generation and propose solutions for the decoder collapse and successful representation learning of multi-relational KGs.