William La Cava

F. O. de Franca, M. Virgolin, M. Kommenda et al. · cambridge, meta-ai

Symbolic regression searches for analytic expressions that accurately describe studied phenomena. The main attraction of this approach is that it returns an interpretable model that can be insightful to users. Historically, the majority of algorithms for symbolic regression have been based on evolutionary algorithms. However, there has been a recent surge of new proposals that instead utilize approaches such as enumeration algorithms, mixed linear integer programming, neural networks, and Bayesian optimization. In order to assess how well these new approaches behave on a set of common challenges often faced in real-world data, we hosted a competition at the 2022 Genetic and Evolutionary Computation Conference consisting of different synthetic and real-world datasets which were blind to entrants. For the real-world track, we assessed interpretability in a realistic way by using a domain expert to judge the trustworthiness of candidate models.We present an in-depth analysis of the results obtained in this competition, discuss current challenges of symbolic regression algorithms and highlight possible improvements for future competitions.

Saleh Afroogh, Seyd Ishtiaque Ahmed, Petra Ahrweiler et al. · cmu

This study provides a cross-disciplinary examination of Explainable Artificial Intelligence (XAI) approaches-focusing on deep neural networks (DNNs) and large language models (LLMs)-and identifies empirical and conceptual limitations in current XAI. We discuss critical symptoms that stem from deeper root causes (i.e., two paradoxes, two conceptual confusions, and five false assumptions). These fundamental problems within the current XAI research field reveal three insights: experimentally, XAI exhibits significant flaws; conceptually, it is paradoxical; and pragmatically, further attempts to reform the paradoxical XAI might exacerbate its confusion-demanding fundamental shifts and new research directions. To move beyond XAI's limitations, we propose a four-pronged synthesized paradigm shift toward reliable and certified AI development. These four components include: verification-focused Interactive AI (IAI) to establish scientific community protocols for certifying AI system performance rather than attempting post-hoc explanations, AI Epistemology for rigorous scientific foundations, User-Sensible AI to create context-aware systems tailored to specific user communities, and Model-Centered Interpretability for faithful technical analysis-together offering comprehensive post-XAI research directions.

William G. La Cava

Improving the fairness of machine learning models is a nuanced task that requires decision makers to reason about multiple, conflicting criteria. The majority of fair machine learning methods transform the error-fairness trade-off into a single objective problem with a parameter controlling the relative importance of error versus fairness. We propose instead to directly optimize the error-fairness tradeoff by using multi-objective optimization. We present a flexible framework for defining the fair machine learning task as a weighted classification problem with multiple cost functions. This framework is agnostic to the underlying prediction model as well as the metrics. We use multiobjective optimization to define the sample weights used in model training for a given machine learner, and adapt the weights to optimize multiple metrics of fairness and accuracy across a set of tasks. To reduce the number of optimized parameters, and to constrain their complexity with respect to population subgroups, we propose a novel meta-model approach that learns to map protected attributes to sample weights, rather than optimizing those weights directly. On a set of real-world problems, this approach outperforms current state-of-the-art methods by finding solution sets with preferable error/fairness trade-offs.

William La Cava, Elle Lett, Guangya Wan

Fair calibration is a widely desirable fairness criteria in risk prediction contexts. One way to measure and achieve fair calibration is with multicalibration. Multicalibration constrains calibration error among flexibly-defined subpopulations while maintaining overall calibration. However, multicalibrated models can exhibit a higher percent calibration error among groups with lower base rates than groups with higher base rates. As a result, it is possible for a decision-maker to learn to trust or distrust model predictions for specific groups. To alleviate this, we propose \emph{proportional multicalibration}, a criteria that constrains the percent calibration error among groups and within prediction bins. We prove that satisfying proportional multicalibration bounds a model's multicalibration as well its \emph{differential calibration}, a fairness criteria that directly measures how closely a model approximates sufficiency. Therefore, proportionally calibrated models limit the ability of decision makers to distinguish between model performance on different patient groups, which may make the models more trustworthy in practice. We provide an efficient algorithm for post-processing risk prediction models for proportional multicalibration and evaluate it empirically. We conduct simulation studies and investigate a real-world application of PMC-postprocessing to prediction of emergency department patient admissions. We observe that proportional multicalibration is a promising criteria for controlling simultaneous measures of calibration fairness of a model over intersectional groups with virtually no cost in terms of classification performance.

William La Cava, Patryk Orzechowski, Bogdan Burlacu et al.

Many promising approaches to symbolic regression have been presented in recent years, yet progress in the field continues to suffer from a lack of uniform, robust, and transparent benchmarking standards. In this paper, we address this shortcoming by introducing an open-source, reproducible benchmarking platform for symbolic regression. We assess 14 symbolic regression methods and 7 machine learning methods on a set of 252 diverse regression problems. Our assessment includes both real-world datasets with no known model form as well as ground-truth benchmark problems, including physics equations and systems of ordinary differential equations. For the real-world datasets, we benchmark the ability of each method to learn models with low error and low complexity relative to state-of-the-art machine learning methods. For the synthetic problems, we assess each method's ability to find exact solutions in the presence of varying levels of noise. Under these controlled experiments, we conclude that the best performing methods for real-world regression combine genetic algorithms with parameter estimation and/or semantic search drivers. When tasked with recovering exact equations in the presence of noise, we find that deep learning and genetic algorithm-based approaches perform similarly. We provide a detailed guide to reproducing this experiment and contributing new methods, and encourage other researchers to collaborate with us on a common and living symbolic regression benchmark.

Joseph D. Romano, Trang T. Le, William La Cava et al.

Motivation: Novel machine learning and statistical modeling studies rely on standardized comparisons to existing methods using well-studied benchmark datasets. Few tools exist that provide rapid access to many of these datasets through a standardized, user-friendly interface that integrates well with popular data science workflows. Results: This release of PMLB provides the largest collection of diverse, public benchmark datasets for evaluating new machine learning and data science methods aggregated in one location. v1.0 introduces a number of critical improvements developed following discussions with the open-source community. Availability: PMLB is available at https://github.com/EpistasisLab/pmlb. Python and R interfaces for PMLB can be installed through the Python Package Index and Comprehensive R Archive Network, respectively.

William La Cava, Tilak Raj Singh, James Taggart et al.

We propose and study a method for learning interpretable representations for the task of regression. Features are represented as networks of multi-type expression trees comprised of activation functions common in neural networks in addition to other elementary functions. Differentiable features are trained via gradient descent, and the performance of features in a linear model is used to weight the rate of change among subcomponents of each representation. The search process maintains an archive of representations with accuracy-complexity trade-offs to assist in generalization and interpretation. We compare several stochastic optimization approaches within this framework. We benchmark these variants on 100 open-source regression problems in comparison to state-of-the-art machine learning approaches. Our main finding is that this approach produces the highest average test scores across problems while producing representations that are orders of magnitude smaller than the next best performing method (gradient boosting). We also report a negative result in which attempts to directly optimize the disentanglement of the representation result in more highly correlated features.

Patryk Orzechowski, William La Cava, Jason H. Moore

In this paper we provide a broad benchmarking of recent genetic programming approaches to symbolic regression in the context of state of the art machine learning approaches. We use a set of nearly 100 regression benchmark problems culled from open source repositories across the web. We conduct a rigorous benchmarking of four recent symbolic regression approaches as well as nine machine learning approaches from scikit-learn. The results suggest that symbolic regression performs strongly compared to state-of-the-art gradient boosting algorithms, although in terms of running times is among the slowest of the available methodologies. We discuss the results in detail and point to future research directions that may allow symbolic regression to gain wider adoption in the machine learning community.

Randal S. Olson, Moshe Sipper, William La Cava et al.

While artificial intelligence (AI) has become widespread, many commercial AI systems are not yet accessible to individual researchers nor the general public due to the deep knowledge of the systems required to use them. We believe that AI has matured to the point where it should be an accessible technology for everyone. We present an ongoing project whose ultimate goal is to deliver an open source, user-friendly AI system that is specialized for machine learning analysis of complex data in the biomedical and health care domains. We discuss how genetic programming can aid in this endeavor, and highlight specific examples where genetic programming has automated machine learning analyses in previous projects.

Guilherme S. Imai Aldeia, Hengzhe Zhang, Geoffrey Bomarito et al.

Symbolic Regression (SR) is a powerful technique for discovering interpretable mathematical expressions. However, benchmarking SR methods remains challenging due to the diversity of algorithms, datasets, and evaluation criteria. In this work, we present an updated version of SRBench. Our benchmark expands the previous one by nearly doubling the number of evaluated methods, refining evaluation metrics, and using improved visualizations of the results to understand the performances. Additionally, we analyze trade-offs between model complexity, accuracy, and energy consumption. Our results show that no single algorithm dominates across all datasets. We propose a call for action from SR community in maintaining and evolving SRBench as a living benchmark that reflects the state-of-the-art in symbolic regression, by standardizing hyperparameter tuning, execution constraints, and computational resource allocation. We also propose deprecation criteria to maintain the benchmark's relevance and discuss best practices for improving SR algorithms, such as adaptive hyperparameter tuning and energy-efficient implementations.

Guilherme Seidyo Imai Aldeia, Fabricio Olivetti de Franca, William G. La Cava

Symbolic regression (SR) searches for parametric models that accurately fit a dataset, prioritizing simplicity and interpretability. Despite this secondary objective, studies point out that the models are often overly complex due to redundant operations, introns, and bloat that arise during the iterative process, and can hinder the search with repeated exploration of bloated segments. Applying a fast heuristic algebraic simplification may not fully simplify the expression and exact methods can be infeasible depending on size or complexity of the expressions. We propose a novel agnostic simplification and bloat control for SR employing an efficient memoization with locality-sensitive hashing (LHS). The idea is that expressions and their sub-expressions traversed during the iterative simplification process are stored in a dictionary using LHS, enabling efficient retrieval of similar structures. We iterate through the expression, replacing subtrees with others of same hash if they result in a smaller expression. Empirical results shows that applying this simplification during evolution performs equal or better than without simplification in minimization of error, significantly reducing the number of nonlinear functions. This technique can learn simplification rules that work in general or for a specific problem, and improves convergence while reducing model complexity.

Mingxuan Liu, Yilin Ning, Haoyuan Wang et al.

As machine learning models become increasingly integrated into healthcare, structural inequities and social biases embedded in clinical data can be perpetuated or even amplified by data-driven models. In survival analysis, censoring and time dynamics can further add complexity to fair model development. Additionally, algorithmic fairness approaches often overlook disparities in cross-group rankings, e.g., high-risk Black patients may be ranked below lower-risk White patients who do not experience the event of mortality. Such misranking can reinforce biological essentialism and undermine equitable care. We propose a Fairness-Aware Survival Modeling (FASM), designed to mitigate algorithmic bias regarding both intra-group and cross-group risk rankings over time. Using breast cancer prognosis as a representative case and applying FASM to SEER breast cancer data, we show that FASM substantially improves fairness while preserving discrimination performance comparable to fairness-unaware survival models. Time-stratified evaluations show that FASM maintains stable fairness over a 10-year horizon, with the greatest improvements observed during the mid-term of follow-up. Our approach enables the development of survival models that prioritize both accuracy and equity in clinical decision-making, advancing fairness as a core principle in clinical care.

Platon Lukyanenko, Joshua Mayourian, Mingxuan Liu et al.

Artificial intelligence applied to electrocardiography (AI-ECG) shows potential for mortality prediction, but heterogeneous approaches and private datasets have limited generalizable insights. To address this, we systematically evaluated model design choices across three large cohorts: Beth Israel Deaconess (MIMIC-IV: n = 795,546 ECGs, United States), Telehealth Network of Minas Gerais (Code-15: n = 345,779, Brazil), and Boston Children's Hospital (BCH: n = 255,379, United States). We evaluated models predicting all-cause mortality, comparing horizon-based classification and deep survival methods with neural architectures including convolutional networks and transformers, benchmarking against demographic-only and gradient boosting baselines. Top models performed well (median concordance: Code-15, 0.83; MIMIC-IV, 0.78; BCH, 0.81). Incorporating age and sex improved performance across all datasets. Classifier-Cox models showed site-dependent sensitivity to horizon choice (median Pearson's R: Code-15, 0.35; MIMIC-IV, -0.71; BCH, 0.37). External validation reduced concordance, and in some cases demographic-only models outperformed externally trained AI-ECG models on Code-15. However, models trained on multi-site data outperformed site-specific models by 5-22%. Findings highlight factors for robust AI-ECG deployment: deep survival methods outperformed horizon-based classifiers, demographic covariates improved predictive performance, classifier-based models required site-specific calibration, and cross-cohort training, even between adult and pediatric cohorts, substantially improved performance. These results emphasize the importance of model type, demographics, and training diversity in developing AI-ECG models reliably applicable across populations.

Shan Chen, Jack Gallifant, Mingye Gao et al.

Large language models (LLMs) are increasingly essential in processing natural languages, yet their application is frequently compromised by biases and inaccuracies originating in their training data. In this study, we introduce Cross-Care, the first benchmark framework dedicated to assessing biases and real world knowledge in LLMs, specifically focusing on the representation of disease prevalence across diverse demographic groups. We systematically evaluate how demographic biases embedded in pre-training corpora like $ThePile$ influence the outputs of LLMs. We expose and quantify discrepancies by juxtaposing these biases against actual disease prevalences in various U.S. demographic groups. Our results highlight substantial misalignment between LLM representation of disease prevalence and real disease prevalence rates across demographic subgroups, indicating a pronounced risk of bias propagation and a lack of real-world grounding for medical applications of LLMs. Furthermore, we observe that various alignment methods minimally resolve inconsistencies in the models' representation of disease prevalence across different languages. For further exploration and analysis, we make all data and a data visualization tool available at: www.crosscare.net.

William La Cava, Heather Williams, Weixuan Fu et al.

Motivation: Many researchers with domain expertise are unable to easily apply machine learning to their bioinformatics data due to a lack of machine learning and/or coding expertise. Methods that have been proposed thus far to automate machine learning mostly require programming experience as well as expert knowledge to tune and apply the algorithms correctly. Here, we study a method of automating biomedical data science using a web-based platform that uses AI to recommend model choices and conduct experiments. We have two goals in mind: first, to make it easy to construct sophisticated models of biomedical processes; and second, to provide a fully automated AI agent that can choose and conduct promising experiments for the user, based on the user's experiments as well as prior knowledge. To validate this framework, we experiment with hundreds of classification problems, comparing to state-of-the-art, automated approaches. Finally, we use this tool to develop predictive models of septic shock in critical care patients. Results: We find that matrix factorization-based recommendation systems outperform meta-learning methods for automating machine learning. This result mirrors the results of earlier recommender systems research in other domains. The proposed AI is competitive with state-of-the-art automated machine learning methods in terms of choosing optimal algorithm configurations for datasets. In our application to prediction of septic shock, the AI-driven analysis produces a competent machine learning model (AUROC 0.85 +/- 0.02) that performs on par with state-of-the-art deep learning results for this task, with much less computational effort.

William La Cava, Christopher Bauer, Jason H. Moore et al.

Electronic health records are an increasingly important resource for understanding the interactions between patient health, environment, and clinical decisions. In this paper we report an empirical study of predictive modeling of several patient outcomes using three state-of-the-art machine learning methods. Our primary goal is to validate the models by interpreting the importance of predictors in the final models. Central to interpretation is the use of feature importance scores, which vary depending on the underlying methodology. In order to assess feature importance, we compared univariate statistical tests, information-theoretic measures, permutation testing, and normalized coefficients from multivariate logistic regression models. In general we found poor correlation between methods in their assessment of feature importance, even when their performance is comparable and relatively good. However, permutation tests applied to random forest and gradient boosting models showed the most agreement, and the importance scores matched the clinical interpretation most frequently.

Ryan J. Urbanowicz, Melissa Meeker, William LaCava et al.

Feature selection plays a critical role in biomedical data mining, driven by increasing feature dimensionality in target problems and growing interest in advanced but computationally expensive methodologies able to model complex associations. Specifically, there is a need for feature selection methods that are computationally efficient, yet sensitive to complex patterns of association, e.g. interactions, so that informative features are not mistakenly eliminated prior to downstream modeling. This paper focuses on Relief-based algorithms (RBAs), a unique family of filter-style feature selection algorithms that have gained appeal by striking an effective balance between these objectives while flexibly adapting to various data characteristics, e.g. classification vs. regression. First, this work broadly examines types of feature selection and defines RBAs within that context. Next, we introduce the original Relief algorithm and associated concepts, emphasizing the intuition behind how it works, how feature weights generated by the algorithm can be interpreted, and why it is sensitive to feature interactions without evaluating combinations of features. Lastly, we include an expansive review of RBA methodological research beyond Relief and its popular descendant, ReliefF. In particular, we characterize branches of RBA research, and provide comparative summaries of RBA algorithms including contributions, strategies, functionality, time complexity, adaptation to key data characteristics, and software availability.

William La Cava, Thomas Helmuth, Lee Spector et al.

Lexicase selection is a parent selection method that considers training cases individually, rather than in aggregate, when performing parent selection. Whereas previous work has demonstrated the ability of lexicase selection to solve difficult problems in program synthesis and symbolic regression, the central goal of this paper is to develop the theoretical underpinnings that explain its performance. To this end, we derive an analytical formula that gives the expected probabilities of selection under lexicase selection, given a population and its behavior. In addition, we expand upon the relation of lexicase selection to many-objective optimization methods to describe the behavior of lexicase selection, which is to select individuals on the boundaries of Pareto fronts in high-dimensional space. We show analytically why lexicase selection performs more poorly for certain sizes of population and training cases, and show why it has been shown to perform more poorly in continuous error spaces. To address this last concern, we propose new variants of epsilon-lexicase selection, a method that modifies the pass condition in lexicase selection to allow near-elite individuals to pass cases, thereby improving selection performance with continuous errors. We show that epsilon-lexicase outperforms several diversity-maintenance strategies on a number of real-world and synthetic regression problems.

Randal S. Olson, William La Cava, Zairah Mustahsan et al.

As the bioinformatics field grows, it must keep pace not only with new data but with new algorithms. Here we contribute a thorough analysis of 13 state-of-the-art, commonly used machine learning algorithms on a set of 165 publicly available classification problems in order to provide data-driven algorithm recommendations to current researchers. We present a number of statistical and visual comparisons of algorithm performance and quantify the effect of model selection and algorithm tuning for each algorithm and dataset. The analysis culminates in the recommendation of five algorithms with hyperparameters that maximize classifier performance across the tested problems, as well as general guidelines for applying machine learning to supervised classification problems.

William La Cava, Jason H. Moore

Recently we proposed a general, ensemble-based feature engineering wrapper (FEW) that was paired with a number of machine learning methods to solve regression problems. Here, we adapt FEW for supervised classification and perform a thorough analysis of fitness and survival methods within this framework. Our tests demonstrate that two fitness metrics, one introduced as an adaptation of the silhouette score, outperform the more commonly used Fisher criterion. We analyze survival methods and demonstrate that $ε$-lexicase survival works best across our test problems, followed by random survival which outperforms both tournament and deterministic crowding. We conduct a benchmark comparison to several classification methods using a large set of problems and show that FEW can improve the best classifier performance in several cases. We show that FEW generates consistent, meaningful features for a biomedical problem with different ML pairings.

Randal S. Olson, William La Cava, Patryk Orzechowski et al.

The selection, development, or comparison of machine learning methods in data mining can be a difficult task based on the target problem and goals of a particular study. Numerous publicly available real-world and simulated benchmark datasets have emerged from different sources, but their organization and adoption as standards have been inconsistent. As such, selecting and curating specific benchmarks remains an unnecessary burden on machine learning practitioners and data scientists. The present study introduces an accessible, curated, and developing public benchmark resource to facilitate identification of the strengths and weaknesses of different machine learning methodologies. We compare meta-features among the current set of benchmark datasets in this resource to characterize the diversity of available data. Finally, we apply a number of established machine learning methods to the entire benchmark suite and analyze how datasets and algorithms cluster in terms of performance. This work is an important first step towards understanding the limitations of popular benchmarking suites and developing a resource that connects existing benchmarking standards to more diverse and efficient standards in the future.