Deploying machine learning models into sensitive domains in our society requires these models to be explainable. Genetic Programming (GP) can offer a way to evolve inherently interpretable expressions. GP-GOMEA is a form of GP that has been found particularly effective at evolving expressions that are accurate yet of limited size and, thus, promote interpretability. Despite this strength, a limitation of GP-GOMEA is template-based. This negatively affects its scalability regarding the arity of operators that can be used, since with increasing operator arity, an increasingly large part of the template tends to go unused. In this paper, we therefore propose two enhancements to GP-GOMEA: (i) semantic subtree inheritance, which performs additional variation steps that consider the semantic context of a subtree, and (ii) greedy child selection, which explicitly considers parts of the template that in standard GP-GOMEA remain unused. We compare different versions of GP-GOMEA regarding search enhancements on a set of continuous and discontinuous regression problems, with varying tree depths and operator sets. Experimental results show that both proposed search enhancements have a generally positive impact on the performance of GP-GOMEA, especially when the set of operators to choose from is large and contains higher-arity operators.
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Gary Lorden provided a number of fundamental and novel insights to sequential hypothesis testing and changepoint detection. In this article we provide an overview of Lorden's contributions in the context of existing results in those areas, and some extensions made possible by Lorden's work, mentioning also areas of application including threat detection in physical-computer systems, near-Earth space informatics, epidemiology, clinical trials, and finance.
Feature models have become a de facto standard for representing variability in software product lines. UVL (Universal Variability Language) is a language which expresses the features, dependencies, and constraints between them. This language is written in plain text and follows a syntactic structure that needs to be processed by a parser. This parser is software with specific syntactic rules that the language must comply with to be processed correctly. Researchers have datasets with numerous feature models. The language description form of these feature models is tied to a version of the parser language. When the parser is updated to support new features or correct previous ones, these feature models are often no longer compatible, generating incompatibilities and inconsistency within the dataset. In this paper, we present UVL Sentinel. This tool analyzes a dataset of feature models in UVL format, generating error analysis reports, describing those errors and, eventually, a syntactic processing that applies the most common solutions. This tool can detect the incompatibilities of the feature models of a dataset when the parser is updated and tries to correct the most common syntactic errors, facilitating the management of the dataset and the adaptation of their models to the new version of the parser. Our tool was evaluated using a dataset of 1,479 UVL models from different sources and helped semi-automatically fix 185 warnings and syntax errors.
Existence of sufficient conditions for unisolvence of Kansa unsymmetric collocation for PDEs is still an open problem. In this paper we make a first step in this direction, proving that unsymmetric collocation matrices with Thin-Plate Splines for the 2D Poisson equation are almost surely nonsingular, when the discretization points are chosen randomly on domains with analytic boundary.
In recent years, machine learning models have achieved success based on the independently and identically distributed assumption. However, this assumption can be easily violated in real-world applications, leading to the Out-of-Distribution (OOD) problem. Understanding how modern over-parameterized DNNs behave under non-trivial natural distributional shifts is essential, as current theoretical understanding is insufficient. Existing theoretical works often provide meaningless results for over-parameterized models in OOD scenarios or even contradict empirical findings. To this end, we are investigating the performance of the over-parameterized model in terms of OOD generalization under the general benign overfitting conditions. Our analysis focuses on a random feature model and examines non-trivial natural distributional shifts, where the benign overfitting estimators demonstrate a constant excess OOD loss, despite achieving zero excess in-distribution (ID) loss. We demonstrate that in this scenario, further increasing the model's parameterization can significantly reduce the OOD loss. Intuitively, the variance term of ID loss remains low due to orthogonality of long-tail features, meaning overfitting noise during training generally doesn't raise testing loss. However, in OOD cases, distributional shift increases the variance term. Thankfully, the inherent shift is unrelated to individual x, maintaining the orthogonality of long-tail features. Expanding the hidden dimension can additionally improve this orthogonality by mapping the features into higher-dimensional spaces, thereby reducing the variance term. We further show that model ensembles also improve OOD loss, akin to increasing model capacity. These insights explain the empirical phenomenon of enhanced OOD generalization through model ensembles, supported by consistent simulations with theoretical results.
We study the Markov chain Monte Carlo (MCMC) estimator for numerical integration for functions that do not need to be square integrable w.r.t. the invariant distribution. For chains with a spectral gap we show that the absolute mean error for $L^p$ functions, with $p \in (1,2)$, decreases like $n^{1/p -1}$, which is known to be the optimal rate. This improves currently known results where an additional parameter $\delta>0$ appears and the convergence is of order $n^{(1+\delta)/p-1}$.
We address the problem of the best uniform approximation of a continuous function on a convex domain. The approximation is by linear combinations of a finite system of functions (not necessarily Chebyshev) under arbitrary linear constraints. By modifying the concept of alternance and of the Remez iterative procedure we present a method, which demonstrates its efficiency in numerical problems. The linear rate of convergence is proved under some favourable assumptions. A special attention is paid to systems of complex exponents, Gaussian functions, lacunar algebraic and trigonometric polynomials. Applications to signal processing, linear ODE, switching dynamical systems, and to Markov-Bernstein type inequalities are considered.
Large language model (LLM) has marked a pivotal moment in the field of machine learning and deep learning. Recently its capability for query planning has been investigated, including both single-modal and multi-modal queries. However, there is no work on the query optimization capability of LLM. As a critical (or could even be the most important) step that significantly impacts the execution performance of the query plan, such analysis and attempts should not be missed. From another aspect, existing query optimizers are usually rule-based or rule-based + cost-based, i.e., they are dependent on manually created rules to complete the query plan rewrite/transformation. Given the fact that modern optimizers include hundreds to thousands of rules, designing a multi-modal query optimizer following a similar way is significantly time-consuming since we will have to enumerate as many multi-modal optimization rules as possible, which has not been well addressed today. In this paper, we investigate the query optimization ability of LLM and use LLM to design LaPuda, a novel LLM and Policy based multi-modal query optimizer. Instead of enumerating specific and detailed rules, LaPuda only needs a few abstract policies to guide LLM in the optimization, by which much time and human effort are saved. Furthermore, to prevent LLM from making mistakes or negative optimization, we borrow the idea of gradient descent and propose a guided cost descent (GCD) algorithm to perform the optimization, such that the optimization can be kept in the correct direction. In our evaluation, our methods consistently outperform the baselines in most cases. For example, the optimized plans generated by our methods result in 1~3x higher execution speed than those by the baselines.
We introduce a 2-dimensional stochastic dominance (2DSD) index to characterize both strict and almost stochastic dominance. Based on this index, we derive an estimator for the minimum violation ratio (MVR), also known as the critical parameter, of the almost stochastic ordering condition between two variables. We determine the asymptotic properties of the empirical 2DSD index and MVR for the most frequently used stochastic orders. We also provide conditions under which the bootstrap estimators of these quantities are strongly consistent. As an application, we develop consistent bootstrap testing procedures for almost stochastic dominance. The performance of the tests is checked via simulations and the analysis of real data.
The goal of explainable Artificial Intelligence (XAI) is to generate human-interpretable explanations, but there are no computationally precise theories of how humans interpret AI generated explanations. The lack of theory means that validation of XAI must be done empirically, on a case-by-case basis, which prevents systematic theory-building in XAI. We propose a psychological theory of how humans draw conclusions from saliency maps, the most common form of XAI explanation, which for the first time allows for precise prediction of explainee inference conditioned on explanation. Our theory posits that absent explanation humans expect the AI to make similar decisions to themselves, and that they interpret an explanation by comparison to the explanations they themselves would give. Comparison is formalized via Shepard's universal law of generalization in a similarity space, a classic theory from cognitive science. A pre-registered user study on AI image classifications with saliency map explanations demonstrate that our theory quantitatively matches participants' predictions of the AI.
Human-in-the-loop aims to train an accurate prediction model with minimum cost by integrating human knowledge and experience. Humans can provide training data for machine learning applications and directly accomplish some tasks that are hard for computers in the pipeline with the help of machine-based approaches. In this paper, we survey existing works on human-in-the-loop from a data perspective and classify them into three categories with a progressive relationship: (1) the work of improving model performance from data processing, (2) the work of improving model performance through interventional model training, and (3) the design of the system independent human-in-the-loop. Using the above categorization, we summarize major approaches in the field, along with their technical strengths/ weaknesses, we have simple classification and discussion in natural language processing, computer vision, and others. Besides, we provide some open challenges and opportunities. This survey intends to provide a high-level summarization for human-in-the-loop and motivates interested readers to consider approaches for designing effective human-in-the-loop solutions.
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