James P. Bagrow

Milo Z. Trujillo, Laurent Hébert-Dufresne, James Bagrow

GitHub has become the central online platform for much of open source, hosting most open source code repositories. With this popularity, the public digital traces of GitHub are now a valuable means to study teamwork and collaboration. In many ways, however, GitHub is a convenience sample, and may not be representative of open source development off the platform. Here we develop a novel, extensive sample of public open source project repositories outside of centralized platforms. We characterized these projects along a number of dimensions, and compare to a time-matched sample of corresponding GitHub projects. Our sample projects tend to have more collaborators, are maintained for longer periods, and tend to be more focused on academic and scientific problems.

Jake Ryland Williams, Eric M. Clark, James P. Bagrow et al.

In an effort to better understand meaning from natural language texts, we explore methods aimed at organizing lexical objects into contexts. A number of these methods for organization fall into a family defined by word ordering. Unlike demographic or spatial partitions of data, these collocation models are of special importance for their universal applicability. While we are interested here in text and have framed our treatment appropriately, our work is potentially applicable to other areas of research (e.g., speech, genomics, and mobility patterns) where one has ordered categorical data, (e.g., sounds, genes, and locations). Our approach focuses on the phrase (whether word or larger) as the primary meaning-bearing lexical unit and object of study. To do so, we employ our previously developed framework for generating word-conserving phrase-frequency data. Upon training our model with the Wiktionary---an extensive, online, collaborative, and open-source dictionary that contains over 100,000 phrasal-definitions---we develop highly effective filters for the identification of meaningful, missing phrase-entries. With our predictions we then engage the editorial community of the Wiktionary and propose short lists of potential missing entries for definition, developing a breakthrough, lexical extraction technique, and expanding our knowledge of the defined English lexicon of phrases.

James Bagrow, Josh Bongard

Efforts to improve Kolmogorov-Arnold networks (KANs) with architectural enhancements have been stymied by the complexity those enhancements bring, undermining the interpretability that makes KANs attractive in the first place. Here we study overprovisioned architectures combined with sparsification to learn compact, interpretable KANs without sacrificing accuracy. Crucially, we focus on differentiable sparsification, turning architecture search into an end-to-end optimization problem. Across function approximation benchmarks, dynamical systems forecasting, and real-world prediction tasks, we demonstrate competitive or superior accuracy while discovering substantially smaller models. Overprovisioning and sparsification are synergistic, with the combination outperforming either alone. The result is a principled path toward models that are both more expressive and more interpretable, addressing a key tension in scientific machine learning.

James Bagrow, Josh Bongard

Kolmogorov-Arnold Networks (KANs) uniquely combine high accuracy with interpretability, making them valuable for scientific modeling. However, it is unclear a priori how deep a network needs to be for any given task, and deeper KANs can be difficult to optimize and interpret. Here we introduce multi-exit KANs, where each layer includes its own prediction branch, enabling the network to make accurate predictions at multiple depths simultaneously. This architecture provides deep supervision that improves training while discovering the right level of model complexity for each task. Multi-exit KANs consistently outperform standard, single-exit versions on synthetic functions, dynamical systems, and real-world datasets. Remarkably, the best predictions often come from earlier, simpler exits, revealing that these networks naturally identify smaller, more parsimonious and interpretable models without sacrificing accuracy. To automate this discovery, we develop a differentiable "learning-to-exit" algorithm that balances contributions from exits during training. Our approach offers scientists a practical way to achieve both high performance and interpretability, addressing a fundamental challenge in machine learning for scientific discovery.

Atoosa Parsa, James Bagrow, Corey S. O'Hern et al.

Externally driven dense packings of particles can exhibit nonlinear wave phenomena that are not described by effective medium theory or linearized approximate models. Such nontrivial wave responses can be exploited to design sound-focusing/scrambling devices, acoustic filters, and analog computational units. At high amplitude vibrations or low confinement pressures, the effect of nonlinear particle contacts becomes increasingly noticeable, and the interplay of nonlinearity, disorder, and discreteness in the system gives rise to remarkable properties, particularly useful in designing structures with exotic properties. In this paper, we build upon the data-driven methods in dynamical system analysis and show that the Koopman spectral theory can be applied to granular crystals, enabling their phase space analysis beyond the linearizable regime and without recourse to any approximations considered in the previous works. We show that a deep neural network can map the dynamics to a latent space where the essential nonlinearity of the granular system unfolds into a high-dimensional linear space. As a proof of concept, we use data from numerical simulations of a two-particle system and evaluate the accuracy of the trajectory predictions under various initial conditions. By incorporating data from experimental measurements, our proposed framework can directly capture the underlying dynamics without imposing any assumptions about the physics model. Spectral analysis of the trained surrogate system can help bridge the gap between the simulation results and the physical realization of granular crystals and facilitate the inverse design of materials with desired behaviors.

James P. Bagrow, Sune Lehmann

The full range of activity in a temporal network is captured in its edge activity data -- time series encoding the tie strengths or on-off dynamics of each edge in the network. However, in many practical applications, edge-level data are unavailable, and the network analyses must rely instead on node activity data which aggregates the edge-activity data and thus is less informative. This raises the question: Is it possible to use the static network to recover the richer edge activities from the node activities? Here we show that recovery is possible, often with a surprising degree of accuracy given how much information is lost, and that the recovered data are useful for subsequent network analysis tasks. Recovery is more difficult when network density increases, either topologically or dynamically, but exploiting dynamical and topological sparsity enables effective solutions to the recovery problem. We formally characterize the difficulty of the recovery problem both theoretically and empirically, proving the conditions under which recovery errors can be bounded and showing that, even when these conditions are not met, good quality solutions can still be derived. Effective recovery carries both promise and peril, as it enables deeper scientific study of complex systems but in the context of social systems also raises privacy concerns when social information can be aggregated across multiple data sources.

Abigail Hotaling, James P. Bagrow

Allowing members of the crowd to propose novel microtasks for one another is an effective way to combine the efficiencies of traditional microtask work with the inventiveness and hypothesis generation potential of human workers. However, microtask proposal leads to a growing set of tasks that may overwhelm limited crowdsourcer resources. Crowdsourcers can employ methods to utilize their resources efficiently, but algorithmic approaches to efficient crowdsourcing generally require a fixed task set of known size. In this paper, we introduce *cost forecasting* as a means for a crowdsourcer to use efficient crowdsourcing algorithms with a growing set of microtasks. Cost forecasting allows the crowdsourcer to decide between eliciting new tasks from the crowd or receiving responses to existing tasks based on whether or not new tasks will cost less to complete than existing tasks, efficiently balancing resources as crowdsourcing occurs. Experiments with real and synthetic crowdsourcing data show that cost forecasting leads to improved accuracy. Accuracy and efficiency gains for crowd-generated microtasks hold the promise to further leverage the creativity and wisdom of the crowd, with applications such as generating more informative and diverse training data for machine learning applications and improving the performance of user-generated content and question-answering platforms.

Andrew J. Becker, James P. Bagrow

Missing data are a concern in many real world data sets and imputation methods are often needed to estimate the values of missing data, but data sets with excessive missingness and high dimensionality challenge most approaches to imputation. Here we show that appropriate feature selection can be an effective preprocessing step for imputation, allowing for more accurate imputation and subsequent model predictions. The key feature of this preprocessing is that it incorporates uncertainty: by accounting for uncertainty due to missingness when selecting features we can reduce the degree of missingness while also limiting the number of uninformative features being used to make predictive models. We introduce a method to perform uncertainty-aware feature selection (UAFS), provide a theoretical motivation, and test UAFS on both real and synthetic problems, demonstrating that across a variety of data sets and levels of missingness we can improve the accuracy of imputations. Improved imputation due to UAFS also results in improved prediction accuracy when performing supervised learning using these imputed data sets. Our UAFS method is general and can be fruitfully coupled with a variety of imputation methods.

Abigail Hotaling, James Bagrow

Allocation strategies improve the efficiency of crowdsourcing by decreasing the work needed to complete individual tasks accurately. However, these algorithms introduce bias by preferentially allocating workers onto easy tasks, leading to sets of completed tasks that are no longer representative of all tasks. This bias challenges inference of problem-wide properties such as typical task difficulty or crowd properties such as worker completion times, important information that goes beyond the crowd responses themselves. Here we study inference about problem properties when using an allocation algorithm to improve crowd efficiency. We introduce Decision-Explicit Probability Sampling (DEPS), a novel method to perform inference of problem properties while accounting for the potential bias introduced by an allocation strategy. Experiments on real and synthetic crowdsourcing data show that DEPS outperforms baseline inference methods while still leveraging the efficiency gains of the allocation method. The ability to perform accurate inference of general properties when using non-representative data allows crowdsourcers to extract more knowledge out of a given crowdsourced dataset.

Daniel Berenberg, James P. Bagrow

Cause-and-effect reasoning, the attribution of effects to causes, is one of the most powerful and unique skills humans possess. Multiple surveys are mapping out causal attributions as networks, but it is unclear how well these efforts can be combined. Further, the total size of the collective causal attribution network held by humans is currently unknown, making it challenging to assess the progress of these surveys. Here we study three causal attribution networks to determine how well they can be combined into a single network. Combining these networks requires dealing with ambiguous nodes, as nodes represent written descriptions of causes and effects and different descriptions may exist for the same concept. We introduce NetFUSES, a method for combining networks with ambiguous nodes. Crucially, treating the different causal attributions networks as independent samples allows us to use their overlap to estimate the total size of the collective causal attribution network. We find that existing surveys capture 5.77% $\pm$ 0.781% of the $\approx$293 000 causes and effects estimated to exist, and 0.198% $\pm$ 0.174% of the $\approx$10 200 000 attributed cause-effect relationships.

Daniel Berenberg, James P. Bagrow

Accurately and efficiently crowdsourcing complex, open-ended tasks can be difficult, as crowd participants tend to favor short, repetitive "microtasks". We study the crowdsourcing of large networks where the crowd provides the network topology via microtasks. Crowds can explore many types of social and information networks, but we focus on the network of causal attributions, an important network that signifies cause-and-effect relationships. We conduct experiments on Amazon Mechanical Turk (AMT) testing how workers propose and validate individual causal relationships and introduce a method for independent crowd workers to explore large networks. The core of the method, Iterative Pathway Refinement, is a theoretically-principled mechanism for efficient exploration via microtasks. We evaluate the method using synthetic networks and apply it on AMT to extract a large-scale causal attribution network, then investigate the structure of this network as well as the activity patterns and efficiency of the workers who constructed this network. Worker interactions reveal important characteristics of causal perception and the network data they generate can improve our understanding of causality and causal inference.

James P. Bagrow, Daniel Berenberg, Joshua Bongard

Many research fields codify their findings in standard formats, often by reporting correlations between quantities of interest. But the space of all testable correlates is far larger than scientific resources can currently address, so the ability to accurately predict correlations would be useful to plan research and allocate resources. Using a dataset of approximately 170,000 correlational findings extracted from leading social science journals, we show that a trained neural network can accurately predict the reported correlations using only the text descriptions of the correlates. Accurate predictive models such as these can guide scientists towards promising untested correlates, better quantify the information gained from new findings, and has implications for moving artificial intelligence systems from predicting structures to predicting relationships in the real world.

James P. Bagrow

Non-experts have long made important contributions to machine learning (ML) by contributing training data, and recent work has shown that non-experts can also help with feature engineering by suggesting novel predictive features. However, non-experts have only contributed features to prediction tasks already posed by experienced ML practitioners. Here we study how non-experts can design prediction tasks themselves, what types of tasks non-experts will design, and whether predictive models can be automatically trained on data sourced for their tasks. We use a crowdsourcing platform where non-experts design predictive tasks that are then categorized and ranked by the crowd. Crowdsourced data are collected for top-ranked tasks and predictive models are then trained and evaluated automatically using those data. We show that individuals without ML experience can collectively construct useful datasets and that predictive models can be learned on these datasets, but challenges remain. The prediction tasks designed by non-experts covered a broad range of domains, from politics and current events to health behavior, demographics, and more. Proper instructions are crucial for non-experts, so we also conducted a randomized trial to understand how different instructions may influence the types of prediction tasks being proposed. In general, understanding better how non-experts can contribute to ML can further leverage advances in Automatic ML and has important implications as ML continues to drive workplace automation.

Mark D. Wagy, Josh C. Bongard, James P. Bagrow et al.

Crowdsourcing has been successfully applied in many domains including astronomy, cryptography and biology. In order to test its potential for useful application in a Smart Grid context, this paper investigates the extent to which a crowd can contribute predictive hypotheses to a model of residential electric energy consumption. In this experiment, the crowd generated hypotheses about factors that make one home different from another in terms of monthly energy usage. To implement this concept, we deployed a web-based system within which 627 residential electricity customers posed 632 questions that they thought predictive of energy usage. While this occurred, the same group provided 110,573 answers to these questions as they accumulated. Thus users both suggested the hypotheses that drive a predictive model and provided the data upon which the model is built. We used the resulting question and answer data to build a predictive model of monthly electric energy consumption, using random forest regression. Because of the sparse nature of the answer data, careful statistical work was needed to ensure that these models are valid. The results indicate that the crowd can generate useful hypotheses, despite the sparse nature of the dataset.

Xipei Liu, James P. Bagrow

Creative tasks such as ideation or question proposal are powerful applications of crowdsourcing, yet the quantity of workers available for addressing practical problems is often insufficient. To enable scalable crowdsourcing thus requires gaining all possible efficiency and information from available workers. One option for text-focused tasks is to allow assistive technology, such as an autocompletion user interface (AUI), to help workers input text responses. But support for the efficacy of AUIs is mixed. Here we designed and conducted a randomized experiment where workers were asked to provide short text responses to given questions. Our experimental goal was to determine if an AUI helps workers respond more quickly and with improved consistency by mitigating typos and misspellings. Surprisingly, we found that neither occurred: workers assigned to the AUI treatment were slower than those assigned to the non-AUI control and their responses were more diverse, not less, than those of the control. Both the lexical and semantic diversities of responses were higher, with the latter measured using word2vec. A crowdsourcer interested in worker speed may want to avoid using an AUI, but using an AUI to boost response diversity may be valuable to crowdsourcers interested in receiving as much novel information from workers as possible.

Thomas C. McAndrew, Elizaveta A. Guseva, James P. Bagrow

Crowdsourcing works by distributing many small tasks to large numbers of workers, yet the true potential of crowdsourcing lies in workers doing more than performing simple tasks---they can apply their experience and creativity to provide new and unexpected information to the crowdsourcer. One such case is when workers not only answer a crowdsourcer's questions but also contribute new questions for subsequent crowd analysis, leading to a growing set of questions. This growth creates an inherent bias for early questions since a question introduced earlier by a worker can be answered by more subsequent workers than a question introduced later. Here we study how to perform efficient crowdsourcing with such growing question sets. By modeling question sets as networks of interrelated questions, we introduce algorithms to help curtail the growth bias by efficiently distributing workers between exploring new questions and addressing current questions. Experiments and simulations demonstrate that these algorithms can efficiently explore an unbounded set of questions without losing confidence in crowd answers.

Thomas C. McAndrew, Joshua C. Bongard, Christopher M. Danforth et al.

Identifying and communicating relationships between causes and effects is important for understanding our world, but is affected by language structure, cognitive and emotional biases, and the properties of the communication medium. Despite the increasing importance of social media, much remains unknown about causal statements made online. To study real-world causal attribution, we extract a large-scale corpus of causal statements made on the Twitter social network platform as well as a comparable random control corpus. We compare causal and control statements using statistical language and sentiment analysis tools. We find that causal statements have a number of significant lexical and grammatical differences compared with controls and tend to be more negative in sentiment than controls. Causal statements made online tend to focus on news and current events, medicine and health, or interpersonal relationships, as shown by topic models. By quantifying the features and potential biases of causality communication, this study improves our understanding of the accuracy of information and opinions found online.

Jake Ryland Williams, James P. Bagrow, Andrew J. Reagan et al.

The task of text segmentation may be undertaken at many levels in text analysis---paragraphs, sentences, words, or even letters. Here, we focus on a relatively fine scale of segmentation, hypothesizing it to be in accord with a stochastic model of language generation, as the smallest scale where independent units of meaning are produced. Our goals in this letter include the development of methods for the segmentation of these minimal independent units, which produce feature-representations of texts that align with the independence assumption of the bag-of-terms model, commonly used for prediction and classification in computational text analysis. We also propose the measurement of texts' association (with respect to realized segmentations) to the model of language generation. We find (1) that our segmentations of phrases exhibit much better associations to the generation model than words and (2), that texts which are well fit are generally topically homogeneous. Because our generative model produces Zipf's law, our study further suggests that Zipf's law may be a consequence of homogeneity in language production.

P. S. Dodds, E. M. Clark, S. Desu et al.

We demonstrate that the concerns expressed by Garcia et al. are misplaced, due to (1) a misreading of our findings in [1]; (2) a widespread failure to examine and present words in support of asserted summary quantities based on word usage frequencies; and (3) a range of misconceptions about word usage frequency, word rank, and expert-constructed word lists. In particular, we show that the English component of our study compares well statistically with two related surveys, that no survey design influence is apparent, and that estimates of measurement error do not explain the positivity biases reported in our work and that of others. We further demonstrate that for the frequency dependence of positivity---of which we explored the nuances in great detail in [1]---Garcia et al. did not perform a reanalysis of our data---they instead carried out an analysis of a different, statistically improper data set and introduced a nonlinearity before performing linear regression.

Jake Ryland Williams, James P. Bagrow, Christopher M. Danforth et al.

Natural languages are full of rules and exceptions. One of the most famous quantitative rules is Zipf's law which states that the frequency of occurrence of a word is approximately inversely proportional to its rank. Though this `law' of ranks has been found to hold across disparate texts and forms of data, analyses of increasingly large corpora over the last 15 years have revealed the existence of two scaling regimes. These regimes have thus far been explained by a hypothesis suggesting a separability of languages into core and non-core lexica. Here, we present and defend an alternative hypothesis, that the two scaling regimes result from the act of aggregating texts. We observe that text mixing leads to an effective decay of word introduction, which we show provides accurate predictions of the location and severity of breaks in scaling. Upon examining large corpora from 10 languages in the Project Gutenberg eBooks collection (eBooks), we find emphatic empirical support for the universality of our claim.

Jake Ryland Williams, Paul R. Lessard, Suma Desu et al.

With Zipf's law being originally and most famously observed for word frequency, it is surprisingly limited in its applicability to human language, holding over no more than three to four orders of magnitude before hitting a clear break in scaling. Here, building on the simple observation that phrases of one or more words comprise the most coherent units of meaning in language, we show empirically that Zipf's law for phrases extends over as many as nine orders of rank magnitude. In doing so, we develop a principled and scalable statistical mechanical method of random text partitioning, which opens up a rich frontier of rigorous text analysis via a rank ordering of mixed length phrases.

Peter Sheridan Dodds, Eric M. Clark, Suma Desu et al.

Using human evaluation of 100,000 words spread across 24 corpora in 10 languages diverse in origin and culture, we present evidence of a deep imprint of human sociality in language, observing that (1) the words of natural human language possess a universal positivity bias; (2) the estimated emotional content of words is consistent between languages under translation; and (3) this positivity bias is strongly independent of frequency of word usage. Alongside these general regularities, we describe inter-language variations in the emotional spectrum of languages which allow us to rank corpora. We also show how our word evaluations can be used to construct physical-like instruments for both real-time and offline measurement of the emotional content of large-scale texts.