Determining potential probability distributions with a given causal graph is vital for causality studies. To bypass the difficulty in characterizing latent variables in a Bayesian network, the nested Markov model provides an elegant algebraic approach by listing exactly all the equality constraints on the observed variables. However, this algebraically motivated causal model comprises distributions outside Bayesian networks, and its physical interpretation remains vague. In this work, we inspect the nested Markov model through the lens of generalized probabilistic theory, an axiomatic framework to describe general physical theories. We prove that all the equality constraints defining the nested Markov model hold valid theory-independently. Yet, we show this model generally contains distributions not implementable even within such relaxed physical theories subjected to merely the relativity principles and mild probabilistic rules. To interpret the origin of such a gap, we establish a new causal model that defines valid distributions as projected from a high-dimensional Bell-type causal structure. The new model unveils inequality constraints induced by relativity principles, or equivalently high-dimensional conditional independences, which are absent in the nested Markov model. Nevertheless, we also notice that the restrictions on states and measurements introduced by the generalized probabilistic theory framework can pose additional inequality constraints beyond the new causal model. As a by-product, we discover a new causal structure exhibiting strict gaps between the distribution sets of a Bayesian network, generalized probabilistic theories, and the nested Markov model. We anticipate our results will enlighten further explorations on the unification of algebraic and physical perspectives of causality.
Integrating robotically driven contact-based material characterization techniques into self-driving laboratories can enhance measurement quality, reliability, and throughput. While deep learning models support robust autonomy, current methods lack reliable pixel-precision positioning and require extensive labeled data. To overcome these challenges, we propose an approach for building self-supervised autonomy into contact-based robotic systems that teach the robot to follow domain expert measurement principles at high-throughputs. Firstly, we design a vision-based, self-supervised convolutional neural network (CNN) architecture that uses differentiable image priors to optimize domain-specific objectives, refining the pixel precision of predicted robot contact poses by 20.0% relative to existing approaches. Secondly, we design a reliable graph-based planner for generating distance-minimizing paths to accelerate the robot measurement throughput and decrease planning variance by 6x. We demonstrate the performance of this approach by autonomously driving a 4-degree-of-freedom robotic probe for 24 hours to characterize semiconductor photoconductivity at 3,025 uniquely predicted poses across a gradient of drop-casted perovskite film compositions, achieving throughputs over 125 measurements per hour. Spatially mapping photoconductivity onto each drop-casted film reveals compositional trends and regions of inhomogeneity, valuable for identifying manufacturing process defects. With this self-supervised CNN-driven robotic system, we enable high-precision and reliable automation of contact-based characterization techniques at high throughputs, thereby allowing the measurement of previously inaccessible yet important semiconductor properties for self-driving laboratories.
Accurate estimates of causal effects play a key role in decision-making across applications such as healthcare, economics, and operations. In the absence of randomized experiments, a common approach to estimating causal effects uses \textit{covariate adjustment}. In this paper, we study covariate adjustment for discrete distributions from the PAC learning perspective, assuming knowledge of a valid adjustment set $\bZ$, which might be high-dimensional. Our first main result PAC-bounds the estimation error of covariate adjustment by a term that is exponential in the size of the adjustment set; it is known that such a dependency is unavoidable even if one only aims to minimize the mean squared error. Motivated by this result, we introduce the notion of an \emph{$\eps$-Markov blanket}, give bounds on the misspecification error of using such a set for covariate adjustment, and provide an algorithm for $\eps$-Markov blanket discovery; our second main result upper bounds the sample complexity of this algorithm. Furthermore, we provide a misspecification error bound and a constraint-based algorithm that allow us to go beyond $\eps$-Markov blankets to even smaller adjustment sets. Our third main result upper bounds the sample complexity of this algorithm, and our final result combines the first three into an overall PAC bound. Altogether, our results highlight that one does not need to perfectly recover causal structure in order to ensure accurate estimates of causal effects.
Emotion and personality are central elements in understanding human psychological states. Emotions reflect an individual subjective experiences, while personality reveals relatively stable behavioral and cognitive patterns. Existing affective computing datasets often annotate emotion and personality traits separately, lacking fine-grained labeling of micro-emotions and emotion intensity in both single-label and multi-label classifications. Chinese emotion datasets are extremely scarce, and datasets capturing Chinese user personality traits are even more limited. To address these gaps, this study collected data from the major social media platform Weibo, screening 11,338 valid users from over 50,000 individuals with diverse MBTI personality labels and acquiring 566,900 posts along with the user MBTI personality tags. Using the EQN method, we compiled a multi-label Chinese affective computing dataset that integrates the same user's personality traits with six emotions and micro-emotions, each annotated with intensity levels. Validation results across multiple NLP classification models demonstrate the dataset strong utility. This dataset is designed to advance machine recognition of complex human emotions and provide data support for research in psychology, education, marketing, finance, and politics.
Large Language Models (LLMs) have demonstrated significant potential in automating software testing, specifically in generating unit test cases. However, the validation of LLM-generated test cases remains a challenge, particularly when the ground truth is unavailable. This paper introduces VALTEST, a novel framework designed to automatically validate test cases generated by LLMs by leveraging token probabilities. We evaluate VALTEST using nine test suites generated from three datasets (HumanEval, MBPP, and LeetCode) across three LLMs (GPT-4o, GPT-3.5-turbo, and LLama3.1 8b). By extracting statistical features from token probabilities, we train a machine learning model to predict test case validity. VALTEST increases the validity rate of test cases by 6.2% to 24%, depending on the dataset and LLM. Our results suggest that token probabilities are reliable indicators for distinguishing between valid and invalid test cases, which provides a robust solution for improving the correctness of LLM-generated test cases in software testing. In addition, we found that replacing the identified invalid test cases by VALTEST, using a Chain-of-Thought prompting results in a more effective test suite while keeping the high validity rates.
This paper presents a stochastic model predictive control (SMPC) algorithm for linear systems subject to additive Gaussian mixture disturbances, with the goal of satisfying chance constraints. We focus on a special case where each Gaussian mixture component has a similar variance. To solve the SMPC problem, we formulate a branch model predictive control (BMPC) problem on simplified dynamics and leverage stochastic simulation relations (SSR). Our contribution is an extension of the SMPC literature to accommodate Gaussian mixture disturbances while retaining recursive feasibility and closed-loop guarantees. We illustrate the retention of guarantees with a case study of vehicle control on an ill-maintained road.
This paper investigates regret minimization, statistical inference, and their interplay in high-dimensional online decision-making based on the sparse linear context bandit model. We integrate the $\varepsilon$-greedy bandit algorithm for decision-making with a hard thresholding algorithm for estimating sparse bandit parameters and introduce an inference framework based on a debiasing method using inverse propensity weighting. Under a margin condition, our method achieves either $O(T^{1/2})$ regret or classical $O(T^{1/2})$-consistent inference, indicating an unavoidable trade-off between exploration and exploitation. If a diverse covariate condition holds, we demonstrate that a pure-greedy bandit algorithm, i.e., exploration-free, combined with a debiased estimator based on average weighting can simultaneously achieve optimal $O(\log T)$ regret and $O(T^{1/2})$-consistent inference. We also show that a simple sample mean estimator can provide valid inference for the optimal policy's value. Numerical simulations and experiments on Warfarin dosing data validate the effectiveness of our methods.
Recent advancements in neural combinatorial optimization (NCO) methods have shown promising results in generating near-optimal solutions without the need for expert-crafted heuristics. However, high performance of these approaches often rely on problem-specific human-expertise-based search after generating candidate solutions, limiting their applicability to commonly solved CO problems such as Traveling Salesman Problem (TSP). In this paper, we present IC/DC, an unsupervised CO framework that directly trains a diffusion model from scratch. We train our model in a self-supervised way to minimize the cost of the solution while adhering to the problem-specific constraints. IC/DC is specialized in addressing CO problems involving two distinct sets of items, and it does not need problem-specific search processes to generate valid solutions. IC/DC employs a novel architecture capable of capturing the intricate relationships between items, and thereby enabling effective optimization in challenging CO scenarios. IC/DC achieves state-of-the-art performance relative to existing NCO methods on the Parallel Machine Scheduling Problem (PMSP) and Asymmetric Traveling Salesman Problem (ATSP).
Model predictive control (MPC) is an industry standard control technique that iteratively solves an open-loop optimization problem to guide a system towards a desired state or trajectory. Consequently, an accurate forward model of system dynamics is critical for the efficacy of MPC and much recent work has been aimed at the use of neural networks to act as data-driven surrogate models to enable MPC. Perhaps the most common network architecture applied to this task is the recurrent neural network (RNN) due to its natural interpretation as a dynamical system. In this work, we assess the ability of RNN variants to both learn the dynamics of benchmark control systems and serve as surrogate models for MPC. We find that echo state networks (ESNs) have a variety of benefits over competing architectures, namely reductions in computational complexity, longer valid prediction times, and reductions in cost of the MPC objective function.
Thanks to unprecedented language understanding and generation capabilities of large language model (LLM), Retrieval-augmented Code Generation (RaCG) has recently been widely utilized among software developers. While this has increased productivity, there are still frequent instances of incorrect codes being provided. In particular, there are cases where plausible yet incorrect codes are generated for queries from users that cannot be answered with the given queries and API descriptions. This study proposes a task for evaluating answerability, which assesses whether valid answers can be generated based on users' queries and retrieved APIs in RaCG. Additionally, we build a benchmark dataset called Retrieval-augmented Code Generability Evaluation (RaCGEval) to evaluate the performance of models performing this task. Experimental results show that this task remains at a very challenging level, with baseline models exhibiting a low performance of 46.7%. Furthermore, this study discusses methods that could significantly improve performance.
Control invariant sets play an important role in safety-critical control and find broad application in numerous fields such as obstacle avoidance for mobile robots. However, finding valid control invariant sets of dynamical systems under input limitations is notoriously difficult. We present an approach to safely expand an initial set while always guaranteeing that the set is control invariant. Specifically, we define an expansion law for the boundary of a set and check for control invariance using Linear Programs (LPs). To verify control invariance on a continuous domain, we leverage recently proposed Lipschitz constants of LPs to transform the problem of continuous verification into a finite number of LPs. Using concepts from differentiable optimization, we derive the safe expansion law of the control invariant set and show how it can be interpreted as a second invariance problem in the space of possible boundaries. Finally, we show how the obtained set can be used to obtain a minimally invasive safety filter in a Control Barrier Function (CBF) framework. Our work is supported by theoretical results as well as numerical examples.
The development of artificial intelligence has made significant contributions to the financial sector. One of the main interests of investors is price predictions. Technical and fundamental analyses, as well as econometric analyses, are conducted for price predictions; recently, the use of AI-based methods has become more prevalent. This study examines daily Dollar/TL exchange rates from January 1, 2020, to October 4, 2024. It has been observed that among artificial intelligence models, random forest, support vector machines, k-nearest neighbors, decision trees, and gradient boosting models were not suitable; however, multilayer perceptron and linear regression models showed appropriate suitability and despite the sharp increase in Dollar/TL rates in Turkey as of 2019, the suitability of valid models has been maintained.
We introduce a new framework for characterizing identified sets of structural and counterfactual parameters in econometric models. By reformulating the identification problem as a set membership question, we leverage the separating hyperplane theorem in the space of observed probability measures to characterize the identified set through the zeros of a discrepancy function with an adversarial game interpretation. The set can be a singleton, resulting in point identification. A feature of many econometric models, with or without distributional assumptions on the error terms, is that the probability measure of observed variables can be expressed as a linear transformation of the probability measure of latent variables. This structure provides a unifying framework and facilitates computation and inference via linear programming. We demonstrate the versatility of our approach by applying it to nonlinear panel models with fixed effects, with parametric and nonparametric error distributions, and across various exogeneity restrictions, including strict and sequential.
The goal of continual learning (CL) is to retain knowledge across tasks, but this conflicts with strict privacy required for sensitive training data that prevents storing or memorising individual samples. To address that, we combine CL and differential privacy (DP). We highlight that failing to account for privacy leakage through the set of labels a model can output can break the privacy of otherwise valid DP algorithms. This is especially relevant in CL. We show that mitigating the issue with a data-independent overly large label space can have minimal negative impact on utility when fine-tuning a pre-trained model under DP, while learning the labels with a separate DP mechanism risks losing small classes.
Adversarial attacks pose significant threats to the reliability and safety of deep learning models, especially in critical domains such as medical imaging. This paper introduces a novel framework that integrates conformal prediction with game-theoretic defensive strategies to enhance model robustness against both known and unknown adversarial perturbations. We address three primary research questions: constructing valid and efficient conformal prediction sets under known attacks (RQ1), ensuring coverage under unknown attacks through conservative thresholding (RQ2), and determining optimal defensive strategies within a zero-sum game framework (RQ3). Our methodology involves training specialized defensive models against specific attack types and employing maximum and minimum classifiers to aggregate defenses effectively. Extensive experiments conducted on the MedMNIST datasets, including PathMNIST, OrganAMNIST, and TissueMNIST, demonstrate that our approach maintains high coverage guarantees while minimizing prediction set sizes. The game-theoretic analysis reveals that the optimal defensive strategy often converges to a singular robust model, outperforming uniform and simple strategies across all evaluated datasets. This work advances the state-of-the-art in uncertainty quantification and adversarial robustness, providing a reliable mechanism for deploying deep learning models in adversarial environments.
We present an explicit construction of a relativistic quantum computing architecture using a variational quantum circuit approach that is shown to allow for universal quantum computing. The variational quantum circuit consists of tunable single-qubit rotations and entangling gates that are implemented successively. The single qubit rotations are parameterized by the proper time intervals of the qubits' trajectories and can be tuned by varying their relativistic motion in spacetime. The entangling layer is mediated by a relativistic quantum field instead of through direct coupling between the qubits. Within this setting, we give a prescription for how to use quantum field-mediated entanglement and manipulation of the relativistic motion of qubits to obtain a universal gate set, for which compact non-perturbative expressions that are valid for general spacetimes are also obtained. We also derive a lower bound on the channel fidelity that shows the existence of parameter regimes in which all entangling operations are effectively unitary, despite the noise generated from the presence of a mediating quantum field. Finally, we consider an explicit implementation of the quantum Fourier transform with relativistic qubits.
Conformal prediction is an uncertainty quantification method that constructs a prediction set for a previously unseen datum, ensuring the true label is included with a predetermined coverage probability. Adaptive conformal prediction has been developed to address data distribution shifts in dynamic environments. However, the efficiency of prediction sets varies depending on the learning model used. Employing a single fixed model may not consistently offer the best performance in dynamic environments with unknown data distribution shifts. To address this issue, we introduce a novel adaptive conformal prediction framework, where the model used for creating prediction sets is selected on the fly from multiple candidate models. The proposed algorithm is proven to achieve strongly adaptive regret over all intervals while maintaining valid coverage. Experiments on real and synthetic datasets corroborate that the proposed approach consistently yields more efficient prediction sets while maintaining valid coverage, outperforming alternative methods.
Counterfactual explanations can be used to interpret and debug text classifiers by producing minimally altered text inputs that change a classifier's output. In this work, we evaluate five methods for generating counterfactual explanations for a BERT text classifier on two datasets using three evaluation metrics. The results of our experiments suggest that established white-box substitution-based methods are effective at generating valid counterfactuals that change the classifier's output. In contrast, newer methods based on large language models (LLMs) excel at producing natural and linguistically plausible text counterfactuals but often fail to generate valid counterfactuals that alter the classifier's output. Based on these results, we recommend developing new counterfactual explanation methods that combine the strengths of established gradient-based approaches and newer LLM-based techniques to generate high-quality, valid, and plausible text counterfactual explanations.
In a split conformal framework with $K$ classes, a calibration sample of $n$ labeled examples is observed for inference on the label of a new unlabeled example. We explore the setting where a `batch' of $m$ independent such unlabeled examples is given, and the goal is to construct a batch prediction set with 1-$\alpha$ coverage. Unlike individual prediction sets, the batch prediction set is a collection of label vectors of size $m$, while the calibration sample consists of univariate labels. A natural approach is to apply the Bonferroni correction, which concatenates individual prediction sets at level $1-\alpha/m$. We propose a uniformly more powerful solution, based on specific combinations of conformal $p$-values that exploit the Simes inequality. We provide a general recipe for valid inference with any combinations of conformal $p$-values, and compare the performance of several useful choices. Intuitively, the pooled evidence of relatively `easy' examples within the batch can help provide narrower batch prediction sets. Additionally, we introduce a more computationally intensive method that aggregates batch scores and can be even more powerful. The theoretical guarantees are established when all examples are independent and identically distributed (iid), as well as more generally when iid is assumed only conditionally within each class. Notably, our results remain valid under label distribution shift, since the distribution of the labels need not be the same in the calibration sample and in the new batch. The effectiveness of the methods is highlighted through illustrative synthetic and real data examples.
Recent methods in quantile regression have adopted a classification perspective to handle challenges posed by heteroscedastic, multimodal, or skewed data by quantizing outputs into fixed bins. Although these regression-as-classification frameworks can capture high-density prediction regions and bypass convex quantile constraints, they are restricted by quantization errors and the curse of dimensionality due to a constant number of bins per dimension. To address these limitations, we introduce a conformalized high-density quantile regression approach with a dynamically adaptive set of prototypes. Our method optimizes the set of prototypes by adaptively adding, deleting, and relocating quantization bins throughout the training process. Moreover, our conformal scheme provides valid coverage guarantees, focusing on regions with the highest probability density. Experiments across diverse datasets and dimensionalities confirm that our method consistently achieves high-quality prediction regions with enhanced coverage and robustness, all while utilizing fewer prototypes and memory, ensuring scalability to higher dimensions. The code is available at https://github.com/batuceng/max_quantile .