Control invariant sets are crucial for various methods that aim to design safe control policies for systems whose state constraints must be satisfied over an indefinite time horizon. In this article, we explore the connections among reachability, control invariance, and Control Barrier Functions (CBFs). Unlike prior formulations based on backward reachability concepts, by examining a forward reachability problem, we are able to establish a strong link between these three concepts. First, our findings show that the inevitable Forward Reachable Tube (FRT), which is the set of states such that every trajectory reaching the FRT must have passed through a given initial set of states, is precisely this initial set of states itself if it is a robust control invariant set with a differentiable boundary. We highlight that this statement may not hold if the boundary is not differentiable. Next, we formulate a differential game between the control and disturbance, where the inevitable FRT is characterized by the zero-superlevel set of the value function. By incorporating a discount factor in the cost function of the game, the barrier constraint of the CBF naturally arises as the constraint that is imposed on the optimal control policy. Combining these results, the value function of our FRT formulation serves as a CBF-like function, and conversely, any valid CBF is also a forward reachability value function inside the control invariant set, thereby revealing the inverse optimality of the CBF. This strong link we establish between the reachability problem and the barrier constraint, while guaranteeing the continuity of the value function, is not achievable by previous backward reachability-based formulations. As such, our work fills a crucial gap in the existing literature that is vital for constructing valid CBFs to ensure safety.
We study the problem of making predictions of an adversarially chosen high-dimensional state that are unbiased subject to an arbitrary collection of conditioning events, with the goal of tailoring these events to downstream decision makers. We give efficient algorithms for solving this problem, as well as a number of applications that stem from choosing an appropriate set of conditioning events. For example, we can efficiently make predictions targeted at polynomially many decision makers, giving each of them optimal swap regret if they best-respond to our predictions. We generalize this to online combinatorial optimization, where the decision makers have a very large action space, to give the first algorithms offering polynomially many decision makers no regret on polynomially many subsequences that may depend on their actions and the context. We apply these results to get efficient no-subsequence-regret algorithms in extensive-form games (EFGs), yielding a new family of regret guarantees for EFGs that generalizes some existing EFG regret notions, e.g. regret to informed causal deviations, and is generally incomparable to other known such notions. Next, we develop a novel transparent alternative to conformal prediction for building valid online adversarial multiclass prediction sets. We produce class scores that downstream algorithms can use for producing valid-coverage prediction sets, as if these scores were the true conditional class probabilities. We show this implies strong conditional validity guarantees including set-size-conditional and multigroup-fair coverage for polynomially many downstream prediction sets. Moreover, our class scores can be guaranteed to have improved $L_2$ loss, cross-entropy loss, and generally any Bregman loss, compared to any collection of benchmark models, yielding a high-dimensional real-valued version of omniprediction.
This article presents a novel method for causal discovery with generalized structural equation models suited for analyzing diverse types of outcomes, including discrete, continuous, and mixed data. Causal discovery often faces challenges due to unmeasured confounders that hinder the identification of causal relationships. The proposed approach addresses this issue by developing two peeling algorithms (bottom-up and top-down) to ascertain causal relationships and valid instruments. This approach first reconstructs a super-graph to represent ancestral relationships between variables, using a peeling algorithm based on nodewise GLM regressions that exploit relationships between primary and instrumental variables. Then, it estimates parent-child effects from the ancestral relationships using another peeling algorithm while deconfounding a child's model with information borrowed from its parents' models. The article offers a theoretical analysis of the proposed approach, which establishes conditions for model identifiability and provides statistical guarantees for accurately discovering parent-child relationships via the peeling algorithms. Furthermore, the article presents numerical experiments showcasing the effectiveness of our approach in comparison to state-of-the-art structure learning methods without confounders. Lastly, it demonstrates an application to Alzheimer's disease (AD), highlighting the utility of the method in constructing gene-to-gene and gene-to-disease regulatory networks involving Single Nucleotide Polymorphisms (SNPs) for healthy and AD subjects.
The anchor-document data derived from web graphs offers a wealth of paired information for training dense retrieval models in an unsupervised manner. However, unsupervised data contains diverse patterns across the web graph and often exhibits significant imbalance, leading to suboptimal performance in underrepresented or difficult groups. In this paper, we introduce WebDRO, an efficient approach for clustering the web graph data and optimizing group weights to enhance the robustness of dense retrieval models. Initially, we build an embedding model for clustering anchor-document pairs. Specifically, we contrastively train the embedding model for link prediction, which guides the embedding model in capturing the document features behind the web graph links. Subsequently, we employ the group distributional robust optimization to recalibrate the weights across different clusters of anchor-document pairs during training retrieval models. During training, we direct the model to assign higher weights to clusters with higher loss and focus more on worst-case scenarios. This approach ensures that the model has strong generalization ability on all data patterns. Our experiments on MS MARCO and BEIR demonstrate that our method can effectively improve retrieval performance in unsupervised training and finetuning settings. Further analysis confirms the stability and validity of group weights learned by WebDRO. The code of this paper can be obtained from https://github.com/Hanpx20/GroupDRO_Dense_Retrieval.
A common technique to reduce model bias in time-series forecasting is to use an ensemble of predictive models and pool their output into an ensemble forecast. In cases where each predictive model has different biases, however, it is not always clear exactly how each model forecast should be weighed during this pooling. We propose a method for pooling that performs a weighted average over candidate model forecasts, where the weights are learned by an attention-based ensemble pooling model. We test this method on two time-series forecasting problems: multi-step forecasting of the dynamics of the non-stationary Lorenz `63 equation, and one-step forecasting of the weekly incident deaths due to COVID-19. We find that while our model achieves excellent valid times when forecasting the non-stationary Lorenz `63 equation, it does not consistently perform better than the existing ensemble pooling when forecasting COVID-19 weekly incident deaths.
We describe the findings of the fourth Nuanced Arabic Dialect Identification Shared Task (NADI 2023). The objective of NADI is to help advance state-of-the-art Arabic NLP by creating opportunities for teams of researchers to collaboratively compete under standardized conditions. It does so with a focus on Arabic dialects, offering novel datasets and defining subtasks that allow for meaningful comparisons between different approaches. NADI 2023 targeted both dialect identification (Subtask 1) and dialect-to-MSA machine translation (Subtask 2 and Subtask 3). A total of 58 unique teams registered for the shared task, of whom 18 teams have participated (with 76 valid submissions during test phase). Among these, 16 teams participated in Subtask 1, 5 participated in Subtask 2, and 3 participated in Subtask 3. The winning teams achieved 87.27 F1 on Subtask 1, 14.76 Bleu in Subtask 2, and 21.10 Bleu in Subtask 3, respectively. Results show that all three subtasks remain challenging, thereby motivating future work in this area. We describe the methods employed by the participating teams and briefly offer an outlook for NADI.
Pose-guided person image synthesis task requires re-rendering a reference image, which should have a photorealistic appearance and flawless pose transfer. Since person images are highly structured, existing approaches require dense connections for complex deformations and occlusions because these are generally handled through multi-level warping and masking in latent space. The feature maps generated by convolutional neural networks do not have equivariance, and hence multi-level warping is required to perform pose alignment. Inspired by the ability of the diffusion model to generate photorealistic images from the given conditional guidance, we propose recurrent pose alignment to provide pose-aligned texture features as conditional guidance. Due to the leakage of the source pose in conditional guidance, we propose gradient guidance from pose interaction fields, which output the distance from the valid pose manifold given a predicted pose as input. This helps in learning plausible pose transfer trajectories that result in photorealism and undistorted texture details. Extensive results on two large-scale benchmarks and a user study demonstrate the ability of our proposed approach to generate photorealistic pose transfer under challenging scenarios. Additionally, we demonstrate the efficiency of gradient guidance in pose-guided image generation on the HumanArt dataset with fine-tuned stable diffusion.
The integration of path reasoning with language modeling in recommender systems has shown promise for enhancing explainability but often struggles with the authenticity of the explanations provided. Traditional models modify their architecture to produce entities and relations alternately--for example, employing separate heads for each in the model--which does not ensure the authenticity of paths reflective of actual Knowledge Graph (KG) connections. This misalignment can lead to user distrust due to the generation of corrupted paths. Addressing this, we introduce PEARLM (Path-based Explainable-Accurate Recommender based on Language Modelling), which innovates with a Knowledge Graph Constraint Decoding (KGCD) mechanism. This mechanism ensures zero incidence of corrupted paths by enforcing adherence to valid KG connections at the decoding level, agnostic of the underlying model architecture. By integrating direct token embedding learning from KG paths, PEARLM not only guarantees the generation of plausible and verifiable explanations but also highly enhances recommendation accuracy. We validate the effectiveness of our approach through a rigorous empirical assessment, employing a newly proposed metric that quantifies the integrity of explanation paths. Our results demonstrate a significant improvement over existing methods, effectively eliminating the generation of inaccurate paths and advancing the state-of-the-art in explainable recommender systems.
Gaussian Process Regression (GPR) is a popular regression method, which unlike most Machine Learning techniques, provides estimates of uncertainty for its predictions. These uncertainty estimates however, are based on the assumption that the model is well-specified, an assumption that is violated in most practical applications, since the required knowledge is rarely available. As a result, the produced uncertainty estimates can become very misleading; for example the prediction intervals (PIs) produced for the 95% confidence level may cover much less than 95% of the true labels. To address this issue, this paper introduces an extension of GPR based on a Machine Learning framework called, Conformal Prediction (CP). This extension guarantees the production of PIs with the required coverage even when the model is completely misspecified. The proposed approach combines the advantages of GPR with the valid coverage guarantee of CP, while the performed experimental results demonstrate its superiority over existing methods.
In the short note, we describe a sampling construction that yields a sequence of graphons converging to a prescribed limit graphon in 1-norm. This convergence is stronger than the convergence in the cut norm, usually used to study graphon sequences. The note also contains errata of the previous version of the note.
Human label variation, or annotation disagreement, exists in many natural language processing (NLP) tasks, including natural language inference (NLI). To gain direct evidence of how NLI label variation arises, we build LiveNLI, an English dataset of 1,415 ecologically valid explanations (annotators explain the NLI labels they chose) for 122 MNLI items (at least 10 explanations per item). The LiveNLI explanations confirm that people can systematically vary on their interpretation and highlight within-label variation: annotators sometimes choose the same label for different reasons. This suggests that explanations are crucial for navigating label interpretations in general. We few-shot prompt large language models to generate explanations but the results are inconsistent: they sometimes produces valid and informative explanations, but it also generates implausible ones that do not support the label, highlighting directions for improvement.
Randomized trials are widely considered as the gold standard for evaluating the effects of decision policies. Trial data is, however, drawn from a population which may differ from the intended target population and this raises a problem of external validity (aka. generalizability). In this paper we seek to use trial data to draw valid inferences about the outcome of a policy on the target population. Additional covariate data from the target population is used to model the sampling of individuals in the trial study. We develop a method that yields certifiably valid trial-based policy evaluations under any specified range of model miscalibrations. The method is nonparametric and the validity is assured even with finite samples. The certified policy evaluations are illustrated using both simulated and real data.
We propose a novel statistical method for testing the results of anomaly detection (AD) under domain adaptation (DA), which we call CAD-DA -- controllable AD under DA. The distinct advantage of the CAD-DA lies in its ability to control the probability of misidentifying anomalies under a pre-specified level $\alpha$ (e.g., 0.05). The challenge within this DA setting is the necessity to account for the influence of DA to ensure the validity of the inference results. Our solution to this challenge leverages the concept of conditional Selective Inference to handle the impact of DA. To our knowledge, this is the first work capable of conducting a valid statistical inference within the context of DA. We evaluate the performance of the CAD-DA method on both synthetic and real-world datasets.
A variety of knowledge graph embedding approaches have been developed. Most of them obtain embeddings by learning the structure of the knowledge graph within a link prediction setting. As a result, the embeddings reflect only the structure of a single knowledge graph, and embeddings for different knowledge graphs are not aligned, e.g., they cannot be used to find similar entities across knowledge graphs via nearest neighbor search. However, knowledge graph embedding applications such as entity disambiguation require a more global representation, i.e., a representation that is valid across multiple sources. We propose to learn universal knowledge graph embeddings from large-scale interlinked knowledge sources. To this end, we fuse large knowledge graphs based on the owl:sameAs relation such that every entity is represented by a unique identity. We instantiate our idea by computing universal embeddings based on DBpedia and Wikidata yielding embeddings for about 180 million entities, 15 thousand relations, and 1.2 billion triples. We believe our computed embeddings will support the emerging field of graph foundation models. Moreover, we develop a convenient API to provide embeddings as a service. Experiments on link prediction suggest that universal knowledge graph embeddings encode better semantics compared to embeddings computed on a single knowledge graph. For reproducibility purposes, we provide our source code and datasets open access.
Research in Text-to-SQL conversion has been largely benchmarked against datasets where each text query corresponds to one correct SQL. However, natural language queries over real-life databases frequently involve significant ambiguity about the intended SQL due to overlapping schema names and multiple confusing relationship paths. To bridge this gap, we develop a novel benchmark called AmbiQT with over 3000 examples where each text is interpretable as two plausible SQLs due to lexical and/or structural ambiguity. When faced with ambiguity, an ideal top-$k$ decoder should generate all valid interpretations for possible disambiguation by the user. We evaluate several Text-to-SQL systems and decoding algorithms, including those employing state-of-the-art LLMs, and find them to be far from this ideal. The primary reason is that the prevalent beam search algorithm and its variants, treat SQL queries as a string and produce unhelpful token-level diversity in the top-$k$. We propose LogicalBeam, a new decoding algorithm that navigates the SQL logic space using a blend of plan-based template generation and constrained infilling. Counterfactually generated plans diversify templates while in-filling with a beam-search that branches solely on schema names provides value diversity. LogicalBeam is up to $2.5$ times more effective than state-of-the-art models at generating all candidate SQLs in the top-$k$ ranked outputs. It also enhances the top-$5$ Exact and Execution Match Accuracies on SPIDER and Kaggle DBQA.
Large language models (LLMs) have demonstrated powerful decision-making and planning capabilities in solving complicated real-world problems. LLM-based autonomous agents can interact with diverse tools (e.g., functional APIs) and generate solution plans that execute a series of API function calls in a step-by-step manner. The multitude of candidate API function calls significantly expands the action space, amplifying the critical need for efficient action space navigation. However, existing methods either struggle with unidirectional exploration in expansive action spaces, trapped into a locally optimal solution, or suffer from exhaustively traversing all potential actions, causing inefficient navigation. To address these issues, we propose ToolChain*, an efficient tree search-based planning algorithm for LLM-based agents. It formulates the entire action space as a decision tree, where each node represents a possible API function call involved in a solution plan. By incorporating the A* search algorithm with task-specific cost function design, it efficiently prunes high-cost branches that may involve incorrect actions, identifying the most low-cost valid path as the solution. Extensive experiments on multiple tool-use and reasoning tasks demonstrate that ToolChain* efficiently balances exploration and exploitation within an expansive action space. It outperforms state-of-the-art baselines on planning and reasoning tasks by 3.1% and 3.5% on average while requiring 7.35x and 2.31x less time, respectively.
Many modern statistical analysis and machine learning applications require training models on sensitive user data. Under a formal definition of privacy protection, differentially private algorithms inject calibrated noise into the confidential data or during the data analysis process to produce privacy-protected datasets or queries. However, restricting access to only privatized data during statistical analysis makes it computationally challenging to make valid statistical inferences. In this work, we propose simulation-based inference methods from privacy-protected datasets. In addition to sequential Monte Carlo approximate Bayesian computation, we adopt neural conditional density estimators as a flexible family of distributions to approximate the posterior distribution of model parameters given the observed private query results. We illustrate our methods on discrete time-series data under an infectious disease model and with ordinary linear regression models. Illustrating the privacy-utility trade-off, our experiments and analysis demonstrate the necessity and feasibility of designing valid statistical inference procedures to correct for biases introduced by the privacy-protection mechanisms.
In drug discovery, it is vital to confirm the predictions of pharmaceutical properties from computational models using costly wet-lab experiments. Hence, obtaining reliable uncertainty estimates is crucial for prioritizing drug molecules for subsequent experimental validation. Conformal Prediction (CP) is a promising tool for creating such prediction sets for molecular properties with a coverage guarantee. However, the exchangeability assumption of CP is often challenged with covariate shift in drug discovery tasks: Most datasets contain limited labeled data, which may not be representative of the vast chemical space from which molecules are drawn. To address this limitation, we propose a method called CoDrug that employs an energy-based model leveraging both training data and unlabelled data, and Kernel Density Estimation (KDE) to assess the densities of a molecule set. The estimated densities are then used to weigh the molecule samples while building prediction sets and rectifying for distribution shift. In extensive experiments involving realistic distribution drifts in various small-molecule drug discovery tasks, we demonstrate the ability of CoDrug to provide valid prediction sets and its utility in addressing the distribution shift arising from de novo drug design models. On average, using CoDrug can reduce the coverage gap by over 35% when compared to conformal prediction sets not adjusted for covariate shift.
Accurate uncertainty quantification in graph neural networks (GNNs) is essential, especially in high-stakes domains where GNNs are frequently employed. Conformal prediction (CP) offers a promising framework for quantifying uncertainty by providing $\textit{valid}$ prediction sets for any black-box model. CP ensures formal probabilistic guarantees that a prediction set contains a true label with a desired probability. However, the size of prediction sets, known as $\textit{inefficiency}$, is influenced by the underlying model and data generating process. On the other hand, Bayesian learning also provides a credible region based on the estimated posterior distribution, but this region is $\textit{well-calibrated}$ only when the model is correctly specified. Building on a recent work that introduced a scaling parameter for constructing valid credible regions from posterior estimate, our study explores the advantages of incorporating a temperature parameter into Bayesian GNNs within CP framework. We empirically demonstrate the existence of temperatures that result in more efficient prediction sets. Furthermore, we conduct an analysis to identify the factors contributing to inefficiency and offer valuable insights into the relationship between CP performance and model calibration.
Metal-organic frameworks (MOFs) are of immense interest in applications such as gas storage and carbon capture due to their exceptional porosity and tunable chemistry. Their modular nature has enabled the use of template-based methods to generate hypothetical MOFs by combining molecular building blocks in accordance with known network topologies. However, the ability of these methods to identify top-performing MOFs is often hindered by the limited diversity of the resulting chemical space. In this work, we propose MOFDiff: a coarse-grained (CG) diffusion model that generates CG MOF structures through a denoising diffusion process over the coordinates and identities of the building blocks. The all-atom MOF structure is then determined through a novel assembly algorithm. Equivariant graph neural networks are used for the diffusion model to respect the permutational and roto-translational symmetries. We comprehensively evaluate our model's capability to generate valid and novel MOF structures and its effectiveness in designing outstanding MOF materials for carbon capture applications with molecular simulations.