Robust Statistical Scaling of Outlier Scores: Improving the Quality of Outlier Probabilities for Outliers (Extended Version)

Outlier detection algorithms typically assign an outlier score to each observation in a dataset, indicating the degree to which an observation is an outlier. However, these scores are often not comparable across algorithms and can be difficult for humans to interpret. Statistical scaling addresses this problem by transforming outlier scores into outlier probabilities without using ground-truth labels, thereby improving interpretability and comparability across algorithms. However, the quality of this transformation can be different for outliers and inliers. Missing outliers in scenarios where they are of particular interest - such as healthcare, finance, or engineering - can be costly or dangerous. Thus, ensuring good probabilities for outliers is essential. This paper argues that statistical scaling, as commonly used in the literature, does not produce equally good probabilities for outliers as for inliers. Therefore, we propose robust statistical scaling, which uses robust estimators to improve the probabilities for outliers. We evaluate several variants of our method against other outlier score transformations for real-world datasets and outlier detection algorithms, where it can improve the probabilities for outliers.

Lexicase-based Selection Methods with Down-sampling for Symbolic Regression Problems: Overview and Benchmark

In recent years, several new lexicase-based selection variants have emerged due to the success of standard lexicase selection in various application domains. For symbolic regression problems, variants that use an epsilon-threshold or batches of training cases, among others, have led to performance improvements. Lately, especially variants that combine lexicase selection and down-sampling strategies have received a lot of attention. This paper evaluates random as well as informed down-sampling in combination with the relevant lexicase-based selection methods on a wide range of symbolic regression problems. In contrast to most work, we not only compare the methods over a given evaluation budget, but also over a given time as time is usually limited in practice. We find that for a given evaluation budget, epsilon-lexicase selection in combination with random or informed down-sampling outperforms all other methods. Only for a rather long running time of 24h, the best performing method is tournament selection in combination with informed down-sampling. If the given running time is very short, lexicase variants using batches of training cases perform best.

Large Language Models Suffer From Their Own Output: An Analysis of the Self-Consuming Training Loop

Large language models (LLM) have become state of the art in many benchmarks and conversational LLM applications like ChatGPT are now widely used by the public. Those LLMs can be used to generate large amounts of content which is posted on the internet to various platforms. As LLMs are trained on datasets usually collected from the internet, this LLM-generated content might be used to train the next generation of LLMs. Therefore, a self-consuming training loop emerges in which new LLM generations are trained on the output from the previous generations. We empirically study this self-consuming training loop using a novel dataset to analytically and accurately measure quality and diversity of generated outputs. We find that this self-consuming training loop initially improves both quality and diversity. However, after a few generations the output inevitably degenerates in diversity. We find that the rate of degeneration depends on the proportion of real and generated data.

Do You Trust ChatGPT? -- Perceived Credibility of Human and AI-Generated Content

This paper examines how individuals perceive the credibility of content originating from human authors versus content generated by large language models, like the GPT language model family that powers ChatGPT, in different user interface versions. Surprisingly, our results demonstrate that regardless of the user interface presentation, participants tend to attribute similar levels of credibility. While participants also do not report any different perceptions of competence and trustworthiness between human and AI-generated content, they rate AI-generated content as being clearer and more engaging. The findings from this study serve as a call for a more discerning approach to evaluating information sources, encouraging users to exercise caution and critical thinking when engaging with content generated by AI systems.

Down-Sampled Epsilon-Lexicase Selection for Real-World Symbolic Regression Problems

Epsilon-lexicase selection is a parent selection method in genetic programming that has been successfully applied to symbolic regression problems. Recently, the combination of random subsampling with lexicase selection significantly improved performance in other genetic programming domains such as program synthesis. However, the influence of subsampling on the solution quality of real-world symbolic regression problems has not yet been studied. In this paper, we propose down-sampled epsilon-lexicase selection which combines epsilon-lexicase selection with random subsampling to improve the performance in the domain of symbolic regression. Therefore, we compare down-sampled epsilon-lexicase with traditional selection methods on common real-world symbolic regression problems and analyze its influence on the properties of the population over a genetic programming run. We find that the diversity is reduced by using down-sampled epsilon-lexicase selection compared to standard epsilon-lexicase selection. This comes along with high hyperselection rates we observe for down-sampled epsilon-lexicase selection. Further, we find that down-sampled epsilon-lexicase selection outperforms the traditional selection methods on all studied problems. Overall, with down-sampled epsilon-lexicase selection we observe an improvement of the solution quality of up to 85% in comparison to standard epsilon-lexicase selection.

MTGP: Combining Metamorphic Testing and Genetic Programming

Genetic programming is an evolutionary approach known for its performance in program synthesis. However, it is not yet mature enough for a practical use in real-world software development, since usually many training cases are required to generate programs that generalize to unseen test cases. As in practice, the training cases have to be expensively hand-labeled by the user, we need an approach to check the program behavior with a lower number of training cases. Metamorphic testing needs no labeled input/output examples. Instead, the program is executed multiple times, first on a given (randomly generated) input, followed by related inputs to check whether certain user-defined relations between the observed outputs hold. In this work, we suggest MTGP, which combines metamorphic testing and genetic programming and study its performance and the generalizability of the generated programs. Further, we analyze how the generalizability depends on the number of given labeled training cases. We find that using metamorphic testing combined with labeled training cases leads to a higher generalization rate than the use of labeled training cases alone in almost all studied configurations. Consequently, we recommend researchers to use metamorphic testing in their systems if the labeling of the training data is expensive.

Informed Down-Sampled Lexicase Selection: Identifying productive training cases for efficient problem solving

Genetic Programming (GP) often uses large training sets and requires all individuals to be evaluated on all training cases during selection. Random down-sampled lexicase selection evaluates individuals on only a random subset of the training cases allowing for more individuals to be explored with the same amount of program executions. However, creating a down-sample randomly might exclude important cases from the current down-sample for a number of generations, while cases that measure the same behavior (synonymous cases) may be overused despite their redundancy. In this work, we introduce Informed Down-Sampled Lexicase Selection. This method leverages population statistics to build down-samples that contain more distinct and therefore informative training cases. Through an empirical investigation across two different GP systems (PushGP and Grammar-Guided GP), we find that informed down-sampling significantly outperforms random down-sampling on a set of contemporary program synthesis benchmark problems. Through an analysis of the created down-samples, we find that important training cases are included in the down-sample consistently across independent evolutionary runs and systems. We hypothesize that this improvement can be attributed to the ability of Informed Down-Sampled Lexicase Selection to maintain more specialist individuals over the course of evolution, while also benefiting from reduced per-evaluation costs.

Choose Your Programming Copilot: A Comparison of the Program Synthesis Performance of GitHub Copilot and Genetic Programming

GitHub Copilot, an extension for the Visual Studio Code development environment powered by the large-scale language model Codex, makes automatic program synthesis available for software developers. This model has been extensively studied in the field of deep learning, however, a comparison to genetic programming, which is also known for its performance in automatic program synthesis, has not yet been carried out. In this paper, we evaluate GitHub Copilot on standard program synthesis benchmark problems and compare the achieved results with those from the genetic programming literature. In addition, we discuss the performance of both approaches. We find that the performance of the two approaches on the benchmark problems is quite similar, however, in comparison to GitHub Copilot, the program synthesis approaches based on genetic programming are not yet mature enough to support programmers in practical software development. Genetic programming usually needs a huge amount of expensive hand-labeled training cases and takes too much time to generate solutions. Furthermore, source code generated by genetic programming approaches is often bloated and difficult to understand. For future work on program synthesis with genetic programming, we suggest researchers to focus on improving the execution time, readability, and usability.

Recent Developments in Program Synthesis with Evolutionary Algorithms

The automatic generation of computer programs is one of the main applications with practical relevance in the field of evolutionary computation. With program synthesis techniques not only software developers could be supported in their everyday work but even users without any programming knowledge could be empowered to automate repetitive tasks and implement their own new functionality. In recent years, many novel program synthesis approaches based on evolutionary algorithms have been proposed and evaluated on common benchmark problems. Therefore, we identify in this work the relevant evolutionary program synthesis approaches and provide an in-depth analysis of their performance. The most influential approaches we identify are stack-based, grammar-guided, as well as linear genetic programming. Further, we find that these approaches perform well on benchmark problems if there is a simple mapping from the given input to the correct output. On problems where this mapping is complex, e.g., if the problem consists of several sub-problems or requires iteration/recursion for a correct solution, results tend to be worse. Consequently, for future work, we encourage researchers not only to use a program's output for assessing the quality of a solution but also the way towards a solution (e.g., correctly solved sub-problems).

The Randomness of Input Data Spaces is an A Priori Predictor for Generalization

Over-parameterized models can perfectly learn various types of data distributions, however, generalization error is usually lower for real data in comparison to artificial data. This suggests that the properties of data distributions have an impact on generalization capability. This work focuses on the search space defined by the input data and assumes that the correlation between labels of neighboring input values influences generalization. If correlation is low, the randomness of the input data space is high leading to high generalization error. We suggest to measure the randomness of an input data space using Maurer's universal. Results for synthetic classification tasks and common image classification benchmarks (MNIST, CIFAR10, and Microsoft's cats vs. dogs data set) find a high correlation between the randomness of input data spaces and the generalization error of deep neural networks for binary classification problems.