Standpoint logic is a recently proposed formalism in the context of knowledge integration, which advocates a multi-perspective approach permitting reasoning with a selection of diverse and possibly conflicting standpoints rather than forcing their unification. In this paper, we introduce nested sequent calculi for propositional standpoint logics--proof systems that manipulate trees whose nodes are multisets of formulae--and show how to automate standpoint reasoning by means of non-deterministic proof-search algorithms. To obtain worst-case complexity-optimal proof-search, we introduce a novel technique in the context of nested sequents, referred to as "coloring," which consists of taking a formula as input, guessing a certain coloring of its subformulae, and then running proof-search in a nested sequent calculus on the colored input. Our technique lets us decide the validity of standpoint formulae in CoNP since proof-search only produces a partial proof relative to each permitted coloring of the input. We show how all partial proofs can be fused together to construct a complete proof when the input is valid, and how certain partial proofs can be transformed into a counter-model when the input is invalid. These "certificates" (i.e. proofs and counter-models) serve as explanations of the (in)validity of the input.
Deep learning has significantly advanced and accelerated de novo molecular generation. Generative networks, namely Variational Autoencoders (VAEs) can not only randomly generate new molecules, but also alter molecular structures to optimize specific chemical properties which are pivotal for drug-discovery. While VAEs have been proposed and researched in the past for pharmaceutical applications, they possess deficiencies which limit their ability to both optimize properties and decode syntactically valid molecules. We present a recurrent, conditional $\beta$-VAE which disentangles the latent space to enhance post hoc molecule optimization. We create a mutual information driven training protocol and data augmentations to both increase molecular validity and promote longer sequence generation. We demonstrate the efficacy of our framework on the ZINC-250k dataset, achieving SOTA unconstrained optimization results on the penalized LogP (pLogP) and QED scores, while also matching current SOTA results for validity, novelty and uniqueness scores for random generation. We match the current SOTA on QED for top-3 molecules at 0.948, while setting a new SOTA for pLogP optimization at 104.29, 90.12, 69.68 and demonstrating improved results on the constrained optimization task.
In this paper, we consider the problem of making distributionally robust, skeptical inferences for the multi-label problem, or more generally for Boolean vectors. By distributionally robust, we mean that we consider a set of possible probability distributions, and by skeptical we understand that we consider as valid only those inferences that are true for every distribution within this set. Such inferences will provide partial predictions whenever the considered set is sufficiently big. We study in particular the Hamming loss case, a common loss function in multi-label problems, showing how skeptical inferences can be made in this setting. Our experimental results are organised in three sections; (1) the first one indicates the gain computational obtained from our theoretical results by using synthetical data sets, (2) the second one indicates that our approaches produce relevant cautiousness on those hard-to-predict instances where its precise counterpart fails, and (3) the last one demonstrates experimentally how our approach copes with imperfect information (generated by a downsampling procedure) better than the partial abstention [31] and the rejection rules.
Medical diagnosis is the process of making a prediction of the disease a patient is likely to have, given a set of symptoms and observations. This requires extensive expert knowledge, in particular when covering a large variety of diseases. Such knowledge can be coded in a knowledge graph -- encompassing diseases, symptoms, and diagnosis paths. Since both the knowledge itself and its encoding can be incomplete, refining the knowledge graph with additional information helps physicians making better predictions. At the same time, for deployment in a hospital, the diagnosis must be explainable and transparent. In this paper, we present an approach using diagnosis paths in a medical knowledge graph. We show that those graphs can be refined using latent representations with RDF2vec, while the final diagnosis is still made in an explainable way. Using both an intrinsic as well as an expert-based evaluation, we show that the embedding-based prediction approach is beneficial for refining the graph with additional valid conditions.
Survivorship bias is the tendency to concentrate on the positive outcomes of a selection process and overlook the results that generate negative outcomes. We observe that this bias could be present in the popular MS MARCO dataset, given that annotators could not find answers to 38--45% of the queries, leading to these queries being discarded in training and evaluation processes. Although we find that some discarded queries in MS MARCO are ill-defined or otherwise unanswerable, many are valid questions that could be answered had the collection been annotated more completely (around two thirds using modern ranking techniques). This survivability problem distorts the MS MARCO collection in several ways. We find that it affects the natural distribution of queries in terms of the type of information needed. When used for evaluation, we find that the bias likely yields a significant distortion of the absolute performance scores observed. Finally, given that MS MARCO is frequently used for model training, we train models based on subsets of MS MARCO that simulates more survivorship bias. We find that models trained in this setting are up to 9.9% worse when evaluated on versions of the dataset with more complete annotations, and up to 3.5% worse at zero-shot transfer. Our findings are complementary to other recent suggestions for further annotation of MS MARCO, but with a focus on discarded queries. Code and data for reproducing the results of this paper are available in an online appendix.
Survival random forest is a popular machine learning tool for modeling censored survival data. However, there is currently no statistically valid and computationally feasible approach for estimating its confidence band. This paper proposes an unbiased confidence band estimation by extending recent developments in infinite-order incomplete U-statistics. The idea is to estimate the variance-covariance matrix of the cumulative hazard function prediction on a grid of time points. We then generate the confidence band by viewing the cumulative hazard function estimation as a Gaussian process whose distribution can be approximated through simulation. This approach is computationally easy to implement when the subsampling size of a tree is no larger than half of the total training sample size. Numerical studies show that our proposed method accurately estimates the confidence band and achieves desired coverage rate. We apply this method to veterans' administration lung cancer data.
High-quality annotated images are significant to deep facial expression recognition (FER) methods. However, uncertain labels, mostly existing in large-scale public datasets, often mislead the training process. In this paper, we achieve uncertain label correction of facial expressions using auxiliary action unit (AU) graphs, called ULC-AG. Specifically, a weighted regularization module is introduced to highlight valid samples and suppress category imbalance in every batch. Based on the latent dependency between emotions and AUs, an auxiliary branch using graph convolutional layers is added to extract the semantic information from graph topologies. Finally, a re-labeling strategy corrects the ambiguous annotations by comparing their feature similarities with semantic templates. Experiments show that our ULC-AG achieves 89.31% and 61.57% accuracy on RAF-DB and AffectNet datasets, respectively, outperforming the baseline and state-of-the-art methods.
This paper focuses on the weakly-supervised audio-visual video parsing task, which aims to recognize all events belonging to each modality and localize their temporal boundaries. This task is challenging because only overall labels indicating the video events are provided for training. However, an event might be labeled but not appear in one of the modalities, which results in a modality-specific noisy label problem. In this work, we propose a training strategy to identify and remove modality-specific noisy labels dynamically. It is motivated by two key observations: 1) networks tend to learn clean samples first; and 2) a labeled event would appear in at least one modality. Specifically, we sort the losses of all instances within a mini-batch individually in each modality, and then select noisy samples according to the relationships between intra-modal and inter-modal losses. Besides, we also propose a simple but valid noise ratio estimation method by calculating the proportion of instances whose confidence is below a preset threshold. Our method makes large improvements over the previous state of the arts (e.g. from 60.0\% to 63.8\% in segment-level visual metric), which demonstrates the effectiveness of our approach. Code and trained models are publicly available at \url{https://github.com/MCG-NJU/JoMoLD}.
This paper tackles the problem of decomposing binary data using matrix factorization. We consider the family of mean-parametrized Bernoulli models, a class of generative models that are well suited for modeling binary data and enables interpretability of the factors. We factorize the Bernoulli parameter and consider an additional Beta prior on one of the factors to further improve the model's expressive power. While similar models have been proposed in the literature, they only exploit the Beta prior as a proxy to ensure a valid Bernoulli parameter in a Bayesian setting; in practice it reduces to a uniform or uninformative prior. Besides, estimation in these models has focused on costly Bayesian inference. In this paper, we propose a simple yet very efficient majorization-minimization algorithm for maximum a posteriori estimation. Our approach leverages the Beta prior whose parameters can be tuned to improve performance in matrix completion tasks. Experiments conducted on three public binary datasets show that our approach offers an excellent trade-off between prediction performance, computational complexity, and interpretability.
Correctly quantifying the robustness of machine learning models is a central aspect in judging their suitability for specific tasks, and ultimately, for generating trust in them. We address the problem of finding the robustness of individual predictions. We show both theoretically and with empirical examples that a method based on counterfactuals that was previously proposed for this is insufficient, as it is not a valid metric for determining the robustness against perturbations that occur ``naturally'', outside specific adversarial attack scenarios. We propose a flexible approach that models possible perturbations in input data individually for each application. This is then combined with a probabilistic approach that computes the likelihood that a ``real-world'' perturbation will change a prediction, thus giving quantitative information of the robustness of individual predictions of the trained machine learning model. The method does not require access to the internals of the classifier and thus in principle works for any black-box model. It is, however, based on Monte-Carlo sampling and thus only suited for input spaces with small dimensions. We illustrate our approach on the Iris and the Ionosphere datasets, on an application predicting fog at an airport, and on analytically solvable cases.
Global IPv6 scanning has always been a challenge for researchers because of the limited network speed and computational power. Target generation algorithms are recently proposed to overcome the problem for Internet assessments by predicting a candidate set to scan. However, IPv6 custom address configuration emerges diverse addressing patterns discouraging algorithmic inference. Widespread IPv6 alias could also mislead the algorithm to discover aliased regions rather than valid host targets. In this paper, we introduce 6GAN, a novel architecture built with Generative Adversarial Net (GAN) and reinforcement learning for multi-pattern target generation. 6GAN forces multiple generators to train with a multi-class discriminator and an alias detector to generate non-aliased active targets with different addressing pattern types. The rewards from the discriminator and the alias detector help supervise the address sequence decision-making process. After adversarial training, 6GAN's generators could keep a strong imitating ability for each pattern and 6GAN's discriminator obtains outstanding pattern discrimination ability with a 0.966 accuracy. Experiments indicate that our work outperformed the state-of-the-art target generation algorithms by reaching a higher-quality candidate set.
Persistent homology is an important methodology from topological data analysis which adapts theory from algebraic topology to data settings and has been successfully implemented in many applications. It produces a statistical summary in the form of a persistence diagram, which captures the shape and size of the data. Despite its widespread use, persistent homology is simply impossible to implement when a dataset is very large. In this paper we address the problem of finding a representative persistence diagram for prohibitively large datasets. We adapt the classical statistical method of bootstrapping, namely, drawing and studying smaller multiple subsamples from the large dataset. We show that the mean of the persistence diagrams of subsamples -- taken as a mean persistence measure computed from the subsamples -- is a valid approximation of the true persistent homology of the larger dataset. We give the rate of convergence of the mean persistence diagram to the true persistence diagram in terms of the number of subsamples and size of each subsample. Given the complex algebraic and geometric nature of persistent homology, we adapt the convexity and stability properties in the space of persistence diagrams together with random set theory to achieve our theoretical results for the general setting of point cloud data. We demonstrate our approach on simulated and real data, including an application of shape clustering on complex large-scale point cloud data.
We prove a central limit theorem for the entropic transportation cost between subgaussian probability measures, centered at the population cost. This is the first result which allows for asymptotically valid inference for entropic optimal transport between measures which are not necessarily discrete. In the compactly supported case, we complement these results with new, faster, convergence rates for the expected entropic transportation cost between empirical measures. Our proof is based on strengthening convergence results for dual solutions to the entropic optimal transport problem.
We present a data-efficient framework for solving sequential decision-making problems which exploits the combination of reinforcement learning (RL) and latent variable generative models. The framework, called GenRL, trains deep policies by introducing an action latent variable such that the feed-forward policy search can be divided into two parts: (i) training a sub-policy that outputs a distribution over the action latent variable given a state of the system, and (ii) unsupervised training of a generative model that outputs a sequence of motor actions conditioned on the latent action variable. GenRL enables safe exploration and alleviates the data-inefficiency problem as it exploits prior knowledge about valid sequences of motor actions. Moreover, we provide a set of measures for evaluation of generative models such that we are able to predict the performance of the RL policy training prior to the actual training on a physical robot. We experimentally determine the characteristics of generative models that have most influence on the performance of the final policy training on two robotics tasks: shooting a hockey puck and throwing a basketball. Furthermore, we empirically demonstrate that GenRL is the only method which can safely and efficiently solve the robotics tasks compared to two state-of-the-art RL methods.
Recent research has demonstrated the importance of flexibly controlling for covariates in instrumental variables estimation. In this paper we study the finite sample and asymptotic properties of various weighting estimators of the local average treatment effect (LATE), motivated by Abadie's (2003) kappa theorem and offering the requisite flexibility relative to standard practice. We argue that two of the estimators under consideration, which are weight normalized, are generally preferable. Several other estimators, which are unnormalized, do not satisfy the properties of scale invariance with respect to the natural logarithm and translation invariance, thereby exhibiting sensitivity to the units of measurement when estimating the LATE in logs and the centering of the outcome variable more generally. We also demonstrate that, when noncompliance is one sided, certain weighting estimators have the advantage of being based on a denominator that is strictly greater than zero by construction. This is the case for only one of the two normalized estimators, and we recommend this estimator for wider use. We illustrate our findings with a simulation study and three empirical applications, which clearly document the sensitivity of unnormalized estimators to how the outcome variable is coded. We implement the proposed estimators in the Stata package kappalate.
This paper highlights the hidden dependence of the basic pricing equation of a multi-period consumption-based asset pricing model on price and payoff autocorrelations. We obtain the approximations of the basic pricing equation that describe the mean price "to-day," mean payoff "next-day," price and payoff volatilities, and price and payoff autocorrelations. The deep conjunction of the consumption-based model with other versions of asset pricing, such as ICAPM, APM, etc. (Cochrane, 2001), emphasizes that our results are valid for other pricing models.
A digital twin contains up-to-date data-driven models of the physical world being studied and can use simulation to optimise the physical world. However, the analysis made by the digital twin is valid and reliable only when the model is equivalent to the physical world. Maintaining such an equivalent model is challenging, especially when the physical systems being modelled are intelligent and autonomous. The paper focuses in particular on digital twin models of intelligent systems where the systems are knowledge-aware but with limited capability. The digital twin improves the acting of the physical system at a meta-level by accumulating more knowledge in the simulated environment. The modelling of such an intelligent physical system requires replicating the knowledge-awareness capability in the virtual space. Novel equivalence maintaining techniques are needed, especially in synchronising the knowledge between the model and the physical system. This paper proposes the notion of knowledge equivalence and an equivalence maintaining approach by knowledge comparison and updates. A quantitative analysis of the proposed approach confirms that compared to state equivalence, knowledge equivalence maintenance can tolerate deviation thus reducing unnecessary updates and achieve more Pareto efficient solutions for the trade-off between update overhead and simulation reliability.
A flexible conformal inference method is developed to construct confidence intervals for the frequencies of queried objects in very large data sets, based on a much smaller sketch of those data. The approach is data-adaptive and requires no knowledge of the data distribution or of the details of the sketching algorithm; instead, it constructs provably valid frequentist confidence intervals under the sole assumption of data exchangeability. Although our solution is broadly applicable, this paper focuses on applications involving the count-min sketch algorithm and a non-linear variation thereof. The performance is compared to that of frequentist and Bayesian alternatives through simulations and experiments with data sets of SARS-CoV-2 DNA sequences and classic English literature.
Wordnets are indispensable tools for various natural language processing applications. Unfortunately, wordnets get outdated, and producing or updating wordnets can be slow and costly in terms of time and resources. This problem intensifies for low-resource languages. This study proposes a method for word sense induction and synset induction using only two linguistic resources, namely, an unlabeled corpus and a sentence embeddings-based language model. The resulting sense inventory and synonym sets can be used in automatically creating a wordnet. We applied this method on a corpus of Filipino text. The sense inventory and synsets were evaluated by matching them with the sense inventory of the machine translated Princeton WordNet, as well as comparing the synsets to the Filipino WordNet. This study empirically shows that the 30% of the induced word senses are valid and 40% of the induced synsets are valid in which 20% are novel synsets.
In this paper, we address the stochastic MPC (SMPC) problem for linear systems, subject to chance state constraints and hard input constraints, under unknown noise distribution. First, we reformulate the chance state constraints as deterministic constraints depending only on explicit noise statistics. Based on these reformulated constraints, we design a distributionally robust and robustly stable benchmark SMPC algorithm for the ideal setting of known noise statistics. Then, we employ this benchmark controller to derive a novel robustly stable adaptive SMPC scheme that learns the necessary noise statistics online, while guaranteeing time-uniform satisfaction of the unknown reformulated state constraints with high probability. The latter is achieved through the use of confidence intervals which rely on the empirical noise statistics and are valid uniformly over time. Moreover, control performance is improved over time as more noise samples are gathered and better estimates of the noise statistics are obtained, given the online adaptation of the estimated reformulated constraints. Additionally, in tracking problems with multiple successive targets our approach leads to an online-enlarged domain of attraction compared to robust tube-based MPC. A numerical simulation of a DC-DC converter is used to demonstrate the effectiveness of the developed methodology.