OpenRaiser/Intern-Atlas huggingface dataset:
Implicitly learning to reason in first-order logic
Venue: Conference NeurIPS 2019
Year: 2019

We consider the problem of answering queries about formulas of first-order logic based on background knowledge partially represented explicitly as other formulas, and partially represented as examples independently drawn from a fixed probability distribution. PAC semantics, introduced by Valiant, is one rigorous, general proposal for learning to reason in formal languages: although weaker than classical entailment, it allows for a powerful model theoretic framework for answering queries while requiring minimal assumptions about the form of the distribution in question. To date, however, the most significant limitation of that approach, and more generally most machine learning approaches with robustness guarantees, is that the logical language is ultimately essentially propositional, with finitely many atoms. Indeed, the theoretical findings on the learning of relational theories in such generality have been resoundingly negative. This is despite the fact that first-order logic is widely argued to be most appropriate for representing human knowledge. In this work, we present a new theoretical approach to robustly learning to reason in first-order logic, and consider universally quantified clauses over a countably infinite domain. Our results exploit symmetries exhibited by constants in the language, and generalize the notion of implicit learnability to show how queries can be computed against (implicitly) learned first-order background knowledge.
Low-Rank Bandit Methods for High-Dimensional Dynamic Pricing
Venue: Conference NeurIPS 2019
Year: 2019

We consider dynamic pricing with many products under an evolving but low-dimensional demand model. Assuming the temporal variation in cross-elasticities exhibits low-rank structure based on fixed (latent) features of the products, we show that the revenue maximization problem reduces to an online bandit convex optimization with side information given by the observed demands. We design dynamic pricing algorithms whose revenue approaches that of the best fixed price vector in hindsight, at a rate that only depends on the intrinsic rank of the demand model and not the number of products. Our approach applies a bandit convex optimization algorithm in a projected low-dimensional space spanned by the latent product features, while simultaneously learning this span via online singular value decomposition of a carefully-crafted matrix containing the observed demands.
Language as an Abstraction for Hierarchical Deep Reinforcement Learning
Venue: Conference NeurIPS 2019
Year: 2019

Solving complex, temporally-extended tasks is a long-standing problem in reinforcement learning (RL). We hypothesize that one critical element of solving such problems is the notion of compositionality. With the ability to learn concepts and sub-skills that can be composed to solve longer tasks, i.e. hierarchical RL, we can acquire temporally-extended behaviors. However, acquiring effective yet general abstractions for hierarchical RL is remarkably challenging. In this paper, we propose to use language as the abstraction, as it provides unique compositional structure, enabling fast learning and combinatorial generalization, while retaining tremendous flexibility, making it suitable for a variety of problems. Our approach learns an instruction-following low-level policy and a high-level policy that can reuse abstractions across tasks, in essence, permitting agents to reason using structured language. To study compositional task learning, we introduce an open-source object interaction environment built using the MuJoCo physics engine and the CLEVR engine. We find that, using our approach, agents can learn to solve to diverse, temporally-extended tasks such as object sorting and multi-object rearrangement, including from raw pixel observations. Our analysis reveals that the compositional nature of language is critical for learning diverse sub-skills and systematically generalizing to new sub-skills in comparison to non-compositional abstractions that use the same supervision.
High-dimensional multivariate forecasting with low-rank Gaussian Copula Processes
Venue: Conference NeurIPS 2019
Year: 2019

Predicting the dependencies between observations from multiple time series is critical for applications such as anomaly detection, financial risk management, causal analysis, or demand forecasting. However, the computational and numerical difficulties of estimating time-varying and high-dimensional covariance matrices often limits existing methods to handling at most a few hundred dimensions or requires making strong assumptions on the dependence between series. We propose to combine an RNN-based time series model with a Gaussian copula process output model with a low-rank covariance structure to reduce the computational complexity and handle non-Gaussian marginal distributions. This permits to drastically reduce the number of parameters and consequently allows the modeling of time-varying correlations of thousands of time series. We show on several real-world datasets that our method provides significant accuracy improvements over state-of-the-art baselines and perform an ablation study analyzing the contributions of the different components of our model.
Optimal Sketching for Kronecker Product Regression and Low Rank Approximation
Venue: Conference NeurIPS 2019
Year: 2019

We study the Kronecker product regression problem, in which the design matrix is a Kronecker product of two or more matrices. Given $A_i \in \mathbb{R}^{n_i \times d_i}$ for $i=1,2,\dots,q$ where $n_i \gg d_i$ for each $i$, and $b \in \mathbb{R}^{n_1 n_2 \cdots n_q}$, let $\mathcal{A} = A_1 \otimes A_2 \otimes \cdots \otimes A_q$. Then for $p \in [1,2]$, the goal is to find $x \in \mathbb{R}^{d_1 \cdots d_q}$ that approximately minimizes $\|\mathcal{A}x - b\|_p$. Recently, Diao, Song, Sun, and Woodruff (AISTATS, 2018) gave an algorithm which is faster than forming the Kronecker product $\mathcal{A}$ Specifically, for $p=2$ their running time is $O(\sum_{i=1}^q \text{nnz}(A_i) + \text{nnz}(b))$, where nnz$(A_i)$ is the number of non-zero entries in $A_i$. Note that nnz$(b)$ can be as large as $n_1 \cdots n_q$. For $p=1,$ $q=2$ and $n_1 = n_2$, they achieve a worse bound of $O(n_1^{3/2} \text{poly}(d_1d_2) + \text{nnz}(b))$. In this work, we provide significantly faster algorithms. For $p=2$, our running time is $O(\sum_{i=1}^q \text{nnz}(A_i) )$, which has no dependence on nnz$(b)$. For $p<2$, our running time is $O(\sum_{i=1}^q \text{nnz}(A_i) + \text{nnz}(b))$, which matches the prior best running time for $p=2$. We also consider the related all-pairs regression problem, where given $A \in \mathbb{R}^{n \times d}, b \in \mathbb{R}^n$, we want to solve $\min_{x} \|\bar{A}x - \bar{b}\|_p$, where $\bar{A} \in \mathbb{R}^{n^2 \times d}, \bar{b} \in \mathbb{R}^{n^2}$ consist of all pairwise differences of the rows of $A,b$. We give an $O(\text{nnz}(A))$ time algorithm for $p \in[1,2]$, improving the $Ω(n^2)$ time needed to form $\bar{A}$. Finally, we initiate the study of Kronecker product low rank and low $t$-rank approximation. For input $\mathcal{A}$ as above, we give $O(\sum_{i=1}^q \text{nnz}(A_i))$ time algorithms, which is much faster than computing $\mathcal{A}$.
Deep Gamblers: Learning to Abstain with Portfolio Theory
Venue: Conference NeurIPS 2019
Year: 2019

We deal with the \textit{selective classification} problem (supervised-learning problem with a rejection option), where we want to achieve the best performance at a certain level of coverage of the data. We transform the original $m$-class classification problem to $(m+1)$-class where the $(m+1)$-th class represents the model abstaining from making a prediction due to disconfidence. Inspired by portfolio theory, we propose a loss function for the selective classification problem based on the doubling rate of gambling. Minimizing this loss function corresponds naturally to maximizing the return of a \textit{horse race}, where a player aims to balance between betting on an outcome (making a prediction) when confident and reserving one's winnings (abstaining) when not confident. This loss function allows us to train neural networks and characterize the disconfidence of prediction in an end-to-end fashion. In comparison with previous methods, our method requires almost no modification to the model inference algorithm or model architecture. Experiments show that our method can identify uncertainty in data points, and achieves strong results on SVHN and CIFAR10 at various coverages of the data.
DRUM: End-To-End Differentiable Rule Mining On Knowledge Graphs
Venue: Conference NeurIPS 2019
Year: 2019

In this paper, we study the problem of learning probabilistic logical rules for inductive and interpretable link prediction. Despite the importance of inductive link prediction, most previous works focused on transductive link prediction and cannot manage previously unseen entities. Moreover, they are black-box models that are not easily explainable for humans. We propose DRUM, a scalable and differentiable approach for mining first-order logical rules from knowledge graphs which resolves these problems. We motivate our method by making a connection between learning confidence scores for each rule and low-rank tensor approximation. DRUM uses bidirectional RNNs to share useful information across the tasks of learning rules for different relations. We also empirically demonstrate the efficiency of DRUM over existing rule mining methods for inductive link prediction on a variety of benchmark datasets.
Fast Low-rank Metric Learning for Large-scale and High-dimensional Data
Venue: Conference NeurIPS 2019
Year: 2019

Low-rank metric learning aims to learn better discrimination of data subject to low-rank constraints. It keeps the intrinsic low-rank structure of datasets and reduces the time cost and memory usage in metric learning. However, it is still a challenge for current methods to handle datasets with both high dimensions and large numbers of samples. To address this issue, we present a novel fast low-rank metric learning (FLRML) method.FLRML casts the low-rank metric learning problem into an unconstrained optimization on the Stiefel manifold, which can be efficiently solved by searching along the descent curves of the manifold.FLRML significantly reduces the complexity and memory usage in optimization, which makes the method scalable to both high dimensions and large numbers of samples.Furthermore, we introduce a mini-batch version of FLRML to make the method scalable to larger datasets which are hard to be loaded and decomposed in limited memory. The outperforming experimental results show that our method is with high accuracy and much faster than the state-of-the-art methods under several benchmarks with large numbers of high-dimensional data. Code has been made available at https://github.com/highan911/FLRML
Unsupervised Emergence of Egocentric Spatial Structure from Sensorimotor Prediction
Venue: Conference NeurIPS 2019
Year: 2019

Despite its omnipresence in robotics application, the nature of spatial knowledge and the mechanisms that underlie its emergence in autonomous agents are still poorly understood. Recent theoretical works suggest that the Euclidean structure of space induces invariants in an agent's raw sensorimotor experience. We hypothesize that capturing these invariants is beneficial for sensorimotor prediction and that, under certain exploratory conditions, a motor representation capturing the structure of the external space should emerge as a byproduct of learning to predict future sensory experiences. We propose a simple sensorimotor predictive scheme, apply it to different agents and types of exploration, and evaluate the pertinence of these hypotheses. We show that a naive agent can capture the topology and metric regularity of its sensor's position in an egocentric spatial frame without any a priori knowledge, nor extraneous supervision.
Generalized Off-Policy Actor-Critic
Venue: Conference NeurIPS 2019
Year: 2019

We propose a new objective, the counterfactual objective, unifying existing objectives for off-policy policy gradient algorithms in the continuing reinforcement learning (RL) setting. Compared to the commonly used excursion objective, which can be misleading about the performance of the target policy when deployed, our new objective better predicts such performance. We prove the Generalized Off-Policy Policy Gradient Theorem to compute the policy gradient of the counterfactual objective and use an emphatic approach to get an unbiased sample from this policy gradient, yielding the Generalized Off-Policy Actor-Critic (Geoff-PAC) algorithm. We demonstrate the merits of Geoff-PAC over existing algorithms in Mujoco robot simulation tasks, the first empirical success of emphatic algorithms in prevailing deep RL benchmarks.
Average Individual Fairness: Algorithms, Generalization and Experiments
Venue: Conference NeurIPS 2019
Year: 2019

We propose a new family of fairness definitions for classification problems that combine some of the best properties of both statistical and individual notions of fairness. We posit not only a distribution over individuals, but also a distribution over (or collection of) classification tasks. We then ask that standard statistics (such as error or false positive/negative rates) be (approximately) equalized across individuals, where the rate is defined as an expectation over the classification tasks. Because we are no longer averaging over coarse groups (such as race or gender), this is a semantically meaningful individual-level constraint. Given a sample of individuals and classification problems, we design an oracle-efficient algorithm (i.e. one that is given access to any standard, fairness-free learning heuristic) for the fair empirical risk minimization task. We also show that given sufficiently many samples, the ERM solution generalizes in two directions: both to new individuals, and to new classification tasks, drawn from their corresponding distributions. Finally we implement our algorithm and empirically verify its effectiveness.
Nonstochastic Multiarmed Bandits with Unrestricted Delays
Venue: Conference NeurIPS 2019
Year: 2019

We investigate multiarmed bandits with delayed feedback, where the delays need neither be identical nor bounded. We first prove that "delayed" Exp3 achieves the $O(\sqrt{(KT + D)\ln K} )$ regret bound conjectured by Cesa-Bianchi et al. [2019] in the case of variable, but bounded delays. Here, $K$ is the number of actions and $D$ is the total delay over $T$ rounds. We then introduce a new algorithm that lifts the requirement of bounded delays by using a wrapper that skips rounds with excessively large delays. The new algorithm maintains the same regret bound, but similar to its predecessor requires prior knowledge of $D$ and $T$. For this algorithm we then construct a novel doubling scheme that forgoes the prior knowledge requirement under the assumption that the delays are available at action time (rather than at loss observation time). This assumption is satisfied in a broad range of applications, including interaction with servers and service providers. The resulting oracle regret bound is of order $\min_β(|S_β|+β\ln K + (KT + D_β)/β)$, where $|S_β|$ is the number of observations with delay exceeding $β$, and $D_β$ is the total delay of observations with delay below $β$. The bound relaxes to $O (\sqrt{(KT + D)\ln K} )$, but we also provide examples where $D_β\ll D$ and the oracle bound has a polynomially better dependence on the problem parameters.
Semi-supervisedly Co-embedding Attributed Networks
Venue: Conference NeurIPS 2019
Year: 2019

Deep generative models (DGMs) have achieved remarkable advances. Semi-supervised variational auto-encoders (SVAE) as a classical DGM offer a principled framework to effectively generalize from small labelled data to large unlabelled ones, but it is difficult to incorporate rich unstructured relationships within the multiple heterogeneous entities. In this paper, to deal with the problem, we present a semi-supervised co-embedding model for attributed networks (SCAN) based on the generalized SVAE for heterogeneous data, which collaboratively learns low-dimensional vector representations of both nodes and attributes for partially labelled attributed networks semi-supervisedly. The node and attribute embeddings obtained in a unified manner by our SCAN can benefit for capturing not only the proximities between nodes but also the affinities between nodes and attributes. Moreover, our model also trains a discriminative network to learn the label predictive distribution of nodes. Experimental results on real-world networks demonstrate that our model yields excellent performance in a number of applications such as attribute inference, user profiling and node classification compared to the state-of-the-art baselines.
Training Image Estimators without Image Ground Truth
Venue: Conference NeurIPS 2019
Year: 2019

Deep neural networks have been very successful in image estimation applications such as compressive-sensing and image restoration, as a means to estimate images from partial, blurry, or otherwise degraded measurements. These networks are trained on a large number of corresponding pairs of measurements and ground-truth images, and thus implicitly learn to exploit domain-specific image statistics. But unlike measurement data, it is often expensive or impractical to collect a large training set of ground-truth images in many application settings. In this paper, we introduce an unsupervised framework for training image estimation networks, from a training set that contains only measurements---with two varied measurements per image---but no ground-truth for the full images desired as output. We demonstrate that our framework can be applied for both regular and blind image estimation tasks, where in the latter case parameters of the measurement model (e.g., the blur kernel) are unknown: during inference, and potentially, also during training. We evaluate our method for training networks for compressive-sensing and blind deconvolution, considering both non-blind and blind training for the latter. Our unsupervised framework yields models that are nearly as accurate as those from fully supervised training, despite not having access to any ground-truth images.
On the Convergence Rate of Training Recurrent Neural Networks
Venue: Conference NeurIPS 2019
Year: 2019

How can local-search methods such as stochastic gradient descent (SGD) avoid bad local minima in training multi-layer neural networks? Why can they fit random labels even given non-convex and non-smooth architectures? Most existing theory only covers networks with one hidden layer, so can we go deeper? In this paper, we focus on recurrent neural networks (RNNs) which are multi-layer networks widely used in natural language processing. They are harder to analyze than feedforward neural networks, because the $\textit{same}$ recurrent unit is repeatedly applied across the entire time horizon of length $L$, which is analogous to feedforward networks of depth $L$. We show when the number of neurons is sufficiently large, meaning polynomial in the training data size and in $L$, then SGD is capable of minimizing the regression loss in the linear convergence rate. This gives theoretical evidence of how RNNs can memorize data. More importantly, in this paper we build general toolkits to analyze multi-layer networks with ReLU activations. For instance, we prove why ReLU activations can prevent exponential gradient explosion or vanishing, and build a perturbation theory to analyze first-order approximation of multi-layer networks.
Factor Group-Sparse Regularization for Efficient Low-Rank Matrix Recovery
Venue: Conference NeurIPS 2019
Year: 2019

This paper develops a new class of nonconvex regularizers for low-rank matrix recovery. Many regularizers are motivated as convex relaxations of the matrix rank function. Our new factor group-sparse regularizers are motivated as a relaxation of the number of nonzero columns in a factorization of the matrix. These nonconvex regularizers are sharper than the nuclear norm; indeed, we show they are related to Schatten-$p$ norms with arbitrarily small $0 < p \leq 1$. Moreover, these factor group-sparse regularizers can be written in a factored form that enables efficient and effective nonconvex optimization; notably, the method does not use singular value decomposition. We provide generalization error bounds for low-rank matrix completion which show improved upper bounds for Schatten-$p$ norm reglarization as $p$ decreases. Compared to the max norm and the factored formulation of the nuclear norm, factor group-sparse regularizers are more efficient, accurate, and robust to the initial guess of rank. Experiments show promising performance of factor group-sparse regularization for low-rank matrix completion and robust principal component analysis.
Hyperbolic Graph Neural Networks
Venue: Conference NeurIPS 2019
Year: 2019

Learning from graph-structured data is an important task in machine learning and artificial intelligence, for which Graph Neural Networks (GNNs) have shown great promise. Motivated by recent advances in geometric representation learning, we propose a novel GNN architecture for learning representations on Riemannian manifolds with differentiable exponential and logarithmic maps. We develop a scalable algorithm for modeling the structural properties of graphs, comparing Euclidean and hyperbolic geometry. In our experiments, we show that hyperbolic GNNs can lead to substantial improvements on various benchmark datasets.
Learning Fairness in Multi-Agent Systems
Venue: Conference NeurIPS 2019
Year: 2019

Fairness is essential for human society, contributing to stability and productivity. Similarly, fairness is also the key for many multi-agent systems. Taking fairness into multi-agent learning could help multi-agent systems become both efficient and stable. However, learning efficiency and fairness simultaneously is a complex, multi-objective, joint-policy optimization. To tackle these difficulties, we propose FEN, a novel hierarchical reinforcement learning model. We first decompose fairness for each agent and propose fair-efficient reward that each agent learns its own policy to optimize. To avoid multi-objective conflict, we design a hierarchy consisting of a controller and several sub-policies, where the controller maximizes the fair-efficient reward by switching among the sub-policies that provides diverse behaviors to interact with the environment. FEN can be trained in a fully decentralized way, making it easy to be deployed in real-world applications. Empirically, we show that FEN easily learns both fairness and efficiency and significantly outperforms baselines in a variety of multi-agent scenarios.