Monte Carlo (MC) sampling is a popular method for estimating the statistics (e.g. expectation and variance) of a random variable. Its slow convergence has led to the emergence of advanced techniques to reduce the variance of the MC estimator for the outputs of computationally expensive solvers. The control variates (CV) method corrects the MC estimator with a term derived from auxiliary random variables that are highly correlated with the original random variable. These auxiliary variables may come from surrogate models. Such a surrogate-based CV strategy is extended here to the multilevel Monte Carlo (MLMC) framework, which relies on a sequence of levels corresponding to numerical simulators with increasing accuracy and computational cost. MLMC combines output samples obtained across levels, into a telescopic sum of differences between MC estimators for successive fidelities. In this paper, we introduce three multilevel variance reduction strategies that rely on surrogate-based CV and MLMC. MLCV is presented as an extension of CV where the correction terms devised from surrogate models for simulators of different levels add up. MLMC-CV improves the MLMC estimator by using a CV based on a surrogate of the correction term at each level. Further variance reduction is achieved by using the surrogate-based CVs of all the levels in the MLMC-MLCV strategy. Alternative solutions that reduce the subset of surrogates used for the multilevel estimation are also introduced. The proposed methods are tested on a test case from the literature consisting of a spectral discretization of an uncertain 1D heat equation, where the statistic of interest is the expected value of the integrated temperature along the domain at a given time. The results are assessed in terms of the accuracy and computational cost of the multilevel estimators, depending on whether the construction of the surrogates, and the associated computational cost, precede the evaluation of the estimator. It was shown that when the lower fidelity outputs are strongly correlated with the high-fidelity outputs, a significant variance reduction is obtained when using surrogate models for the coarser levels only. It was also shown that taking advantage of pre-existing surrogate models proves to be an even more efficient strategy.
Latest methods for visual counterfactual explanations (VCE) harness the power of deep generative models to synthesize new examples of high-dimensional images of impressive quality. However, it is currently difficult to compare the performance of these VCE methods as the evaluation procedures largely vary and often boil down to visual inspection of individual examples and small scale user studies. In this work, we propose a framework for systematic, quantitative evaluation of the VCE methods and a minimal set of metrics to be used. We use this framework to explore the effects of certain crucial design choices in the latest diffusion-based generative models for VCEs of natural image classification (ImageNet). We conduct a battery of ablation-like experiments, generating thousands of VCEs for a suite of classifiers of various complexity, accuracy and robustness. Our findings suggest multiple directions for future advancements and improvements of VCE methods. By sharing our methodology and our approach to tackle the computational challenges of such a study on a limited hardware setup (including the complete code base), we offer a valuable guidance for researchers in the field fostering consistency and transparency in the assessment of counterfactual explanations.
The massive successes of large language models (LLMs) encourage the emerging exploration of LLM-augmented Autonomous Agents (LAAs). An LAA is able to generate actions with its core LLM and interact with environments, which facilitates the ability to resolve complex tasks by conditioning on past interactions such as observations and actions. Since the investigation of LAA is still very recent, limited explorations are available. Therefore, we provide a comprehensive comparison of LAA in terms of both agent architectures and LLM backbones. Additionally, we propose a new strategy to orchestrate multiple LAAs such that each labor LAA focuses on one type of action, \textit{i.e.} BOLAA, where a controller manages the communication among multiple agents. We conduct simulations on both decision-making and multi-step reasoning environments, which comprehensively justify the capacity of LAAs. Our performance results provide quantitative suggestions for designing LAA architectures and the optimal choice of LLMs, as well as the compatibility of both. We release our implementation code of LAAs to the public at \url{//github.com/salesforce/BOLAA}.
Causal Machine Learning (CausalML) is an umbrella term for machine learning methods that formalize the data-generation process as a structural causal model (SCM). This allows one to reason about the effects of changes to this process (i.e., interventions) and what would have happened in hindsight (i.e., counterfactuals). We categorize work in \causalml into five groups according to the problems they tackle: (1) causal supervised learning, (2) causal generative modeling, (3) causal explanations, (4) causal fairness, (5) causal reinforcement learning. For each category, we systematically compare its methods and point out open problems. Further, we review modality-specific applications in computer vision, natural language processing, and graph representation learning. Finally, we provide an overview of causal benchmarks and a critical discussion of the state of this nascent field, including recommendations for future work.
This PhD thesis contains several contributions to the field of statistical causal modeling. Statistical causal models are statistical models embedded with causal assumptions that allow for the inference and reasoning about the behavior of stochastic systems affected by external manipulation (interventions). This thesis contributes to the research areas concerning the estimation of causal effects, causal structure learning, and distributionally robust (out-of-distribution generalizing) prediction methods. We present novel and consistent linear and non-linear causal effects estimators in instrumental variable settings that employ data-dependent mean squared prediction error regularization. Our proposed estimators show, in certain settings, mean squared error improvements compared to both canonical and state-of-the-art estimators. We show that recent research on distributionally robust prediction methods has connections to well-studied estimators from econometrics. This connection leads us to prove that general K-class estimators possess distributional robustness properties. We, furthermore, propose a general framework for distributional robustness with respect to intervention-induced distributions. In this framework, we derive sufficient conditions for the identifiability of distributionally robust prediction methods and present impossibility results that show the necessity of several of these conditions. We present a new structure learning method applicable in additive noise models with directed trees as causal graphs. We prove consistency in a vanishing identifiability setup and provide a method for testing substructure hypotheses with asymptotic family-wise error control that remains valid post-selection. Finally, we present heuristic ideas for learning summary graphs of nonlinear time-series models.
Graph Convolutional Network (GCN) has achieved extraordinary success in learning effective task-specific representations of nodes in graphs. However, regarding Heterogeneous Information Network (HIN), existing HIN-oriented GCN methods still suffer from two deficiencies: (1) they cannot flexibly explore all possible meta-paths and extract the most useful ones for a target object, which hinders both effectiveness and interpretability; (2) they often need to generate intermediate meta-path based dense graphs, which leads to high computational complexity. To address the above issues, we propose an interpretable and efficient Heterogeneous Graph Convolutional Network (ie-HGCN) to learn the representations of objects in HINs. It is designed as a hierarchical aggregation architecture, i.e., object-level aggregation first, followed by type-level aggregation. The novel architecture can automatically extract useful meta-paths for each object from all possible meta-paths (within a length limit), which brings good model interpretability. It can also reduce the computational cost by avoiding intermediate HIN transformation and neighborhood attention. We provide theoretical analysis about the proposed ie-HGCN in terms of evaluating the usefulness of all possible meta-paths, its connection to the spectral graph convolution on HINs, and its quasi-linear time complexity. Extensive experiments on three real network datasets demonstrate the superiority of ie-HGCN over the state-of-the-art methods.
Few-shot Knowledge Graph (KG) completion is a focus of current research, where each task aims at querying unseen facts of a relation given its few-shot reference entity pairs. Recent attempts solve this problem by learning static representations of entities and references, ignoring their dynamic properties, i.e., entities may exhibit diverse roles within task relations, and references may make different contributions to queries. This work proposes an adaptive attentional network for few-shot KG completion by learning adaptive entity and reference representations. Specifically, entities are modeled by an adaptive neighbor encoder to discern their task-oriented roles, while references are modeled by an adaptive query-aware aggregator to differentiate their contributions. Through the attention mechanism, both entities and references can capture their fine-grained semantic meanings, and thus render more expressive representations. This will be more predictive for knowledge acquisition in the few-shot scenario. Evaluation in link prediction on two public datasets shows that our approach achieves new state-of-the-art results with different few-shot sizes.
The recent proliferation of knowledge graphs (KGs) coupled with incomplete or partial information, in the form of missing relations (links) between entities, has fueled a lot of research on knowledge base completion (also known as relation prediction). Several recent works suggest that convolutional neural network (CNN) based models generate richer and more expressive feature embeddings and hence also perform well on relation prediction. However, we observe that these KG embeddings treat triples independently and thus fail to cover the complex and hidden information that is inherently implicit in the local neighborhood surrounding a triple. To this effect, our paper proposes a novel attention based feature embedding that captures both entity and relation features in any given entity's neighborhood. Additionally, we also encapsulate relation clusters and multihop relations in our model. Our empirical study offers insights into the efficacy of our attention based model and we show marked performance gains in comparison to state of the art methods on all datasets.
Recommender systems are widely used in big information-based companies such as Google, Twitter, LinkedIn, and Netflix. A recommender system deals with the problem of information overload by filtering important information fragments according to users' preferences. In light of the increasing success of deep learning, recent studies have proved the benefits of using deep learning in various recommendation tasks. However, most proposed techniques only aim to target individuals, which cannot be efficiently applied in group recommendation. In this paper, we propose a deep learning architecture to solve the group recommendation problem. On the one hand, as different individual preferences in a group necessitate preference trade-offs in making group recommendations, it is essential that the recommendation model can discover substitutes among user behaviors. On the other hand, it has been observed that a user as an individual and as a group member behaves differently. To tackle such problems, we propose using an attention mechanism to capture the impact of each user in a group. Specifically, our model automatically learns the influence weight of each user in a group and recommends items to the group based on its members' weighted preferences. We conduct extensive experiments on four datasets. Our model significantly outperforms baseline methods and shows promising results in applying deep learning to the group recommendation problem.
Recently, ensemble has been applied to deep metric learning to yield state-of-the-art results. Deep metric learning aims to learn deep neural networks for feature embeddings, distances of which satisfy given constraint. In deep metric learning, ensemble takes average of distances learned by multiple learners. As one important aspect of ensemble, the learners should be diverse in their feature embeddings. To this end, we propose an attention-based ensemble, which uses multiple attention masks, so that each learner can attend to different parts of the object. We also propose a divergence loss, which encourages diversity among the learners. The proposed method is applied to the standard benchmarks of deep metric learning and experimental results show that it outperforms the state-of-the-art methods by a significant margin on image retrieval tasks.
Attention mechanism has been used as an ancillary means to help RNN or CNN. However, the Transformer (Vaswani et al., 2017) recently recorded the state-of-the-art performance in machine translation with a dramatic reduction in training time by solely using attention. Motivated by the Transformer, Directional Self Attention Network (Shen et al., 2017), a fully attention-based sentence encoder, was proposed. It showed good performance with various data by using forward and backward directional information in a sentence. But in their study, not considered at all was the distance between words, an important feature when learning the local dependency to help understand the context of input text. We propose Distance-based Self-Attention Network, which considers the word distance by using a simple distance mask in order to model the local dependency without losing the ability of modeling global dependency which attention has inherent. Our model shows good performance with NLI data, and it records the new state-of-the-art result with SNLI data. Additionally, we show that our model has a strength in long sentences or documents.