Christopher Griffin

Christopher Griffin, Trevor Karn, Benjamin Apple · apple-ml

We specialize techniques from topological data analysis to the problem of characterizing the topological complexity (as defined in the body of the paper) of a multi-class data set. As a by-product, a topological classifier is defined that uses an open sub-covering of the data set. This sub-covering can be used to construct a simplicial complex whose topological features (e.g., Betti numbers) provide information about the classification problem. We use these topological constructs to study the impact of topological complexity on learning in feedforward deep neural networks (DNNs). We hypothesize that topological complexity is negatively correlated with the ability of a fully connected feedforward deep neural network to learn to classify data correctly. We evaluate our topological classification algorithm on multiple constructed and open source data sets. We also validate our hypothesis regarding the relationship between topological complexity and learning in DNN's on multiple data sets.

Tatiana Chakravorti, Robert Fraleigh, Timothy Fritton et al.

We present a prototype hybrid prediction market and demonstrate the avenue it represents for meaningful human-AI collaboration. We build on prior work proposing artificial prediction markets as a novel machine-learning algorithm. In an artificial prediction market, trained AI agents buy and sell outcomes of future events. Classification decisions can be framed as outcomes of future events, and accordingly, the price of an asset corresponding to a given classification outcome can be taken as a proxy for the confidence of the system in that decision. By embedding human participants in these markets alongside bot traders, we can bring together insights from both. In this paper, we detail pilot studies with prototype hybrid markets for the prediction of replication study outcomes. We highlight challenges and opportunities, share insights from semi-structured interviews with hybrid market participants, and outline a vision for ongoing and future work.

Shaun Lichter, Christopher Griffin, Terry Friesz

We model the formation of networks as the result of a game where by players act selfishly to get the portfolio of links they desire most. The integration of player strategies into the network formation model is appropriate for organizational networks because in these smaller networks, dynamics are not random, but the result of intentional actions carried through by players maximizing their own objectives. This model is a better framework for the analysis of influences upon a network because it integrates the strategies of the players involved. We present an Integer Program that calculates the price of anarchy of this game by finding the worst stable graph and the best coordinated graph for this game. We simulate the formation of the network and calculated the simulated price of anarchy, which we find tends to be rather low.

Shaun Lichter, Terry Friesz, Christopher Griffin

Recently, it has been shown that networks with an arbitrary degree sequence may be a stable solution to a network formation game. Further, in recent years there has been a rise in the number of firms participating in collaborative efforts. In this paper, we show conditions under which a graph with an arbitrary degree sequence is admitted as a stable firm collaboration graph.

Tatiana Chakravorti, Robert Fraleigh, Timothy Fritton et al.

Determining whether published scientific findings can successfully be replicated is a long-standing challenge in the empirical sciences. Existing approaches for replicability assessment typically rely either on human judgment, i.e., creative assembly of human experts, or on machine learning models trained on paper content metadata. While both approaches have demonstrated value, each also has important limitations. Human forecasts can be influenced by cognitive biases and narrow exposure to the research literature, while automated assessments often struggle to capture contextual cues and subtle signals of credibility. In this paper, we examine a hybrid approach. Specifically, we introduce a hybrid prediction market in which algorithmic agents trade alongside human participants to jointly estimate the likelihood that a published scientific finding will be corroborated via the outcome of a controlled replication study. Agents are trained on outcomes from hundreds of prior replication studies while human participants contribute domain knowledge through real-time trading. We evaluate this hybrid approach through multiple live experiments involving participants from different academic disciplines and compare its performance to artificial-only and human-only baselines. Our results show that, except for a few cases, hybrid markets match or outperform artificial prediction markets, producing more accurate and reliable replication forecasts.

Nishanth Nakshatri, Arjun Menon, C. Lee Giles et al.

We present a synthetic prediction market whose agent purchase logic is defined using a sigmoid transformation of a convex semi-algebraic set defined in feature space. Asset prices are determined by a logarithmic scoring market rule. Time varying asset prices affect the structure of the semi-algebraic sets leading to time-varying agent purchase rules. We show that under certain assumptions on the underlying geometry, the resulting synthetic prediction market can be used to arbitrarily closely approximate a binary function defined on a set of input data. We also provide sufficient conditions for market convergence and show that under certain instances markets can exhibit limit cycles in asset spot price. We provide an evolutionary algorithm for training agent parameters to allow a market to model the distribution of a given data set and illustrate the market approximation using two open source data sets. Results are compared to standard machine learning methods.

Sarah Rajtmajer, Christopher Griffin, Jian Wu et al.

Explainably estimating confidence in published scholarly work offers opportunity for faster and more robust scientific progress. We develop a synthetic prediction market to assess the credibility of published claims in the social and behavioral sciences literature. We demonstrate our system and detail our findings using a collection of known replication projects. We suggest that this work lays the foundation for a research agenda that creatively uses AI for peer review.

Trevor K. Karn, Steven Petrone, Christopher Griffin

In this paper we develop a kernel density estimation (KDE) approach to modeling and forecasting recurrent trajectories on a compact manifold. For the purposes of this paper, a trajectory is a sequence of coordinates in a phase space defined by an underlying hidden dynamical system. Our work is inspired by earlier work on the use of KDE to detect shipping anomalies using high-density, high-quality automated information system (AIS) data as well as our own earlier work in trajectory modeling. We focus specifically on the sparse, noisy trajectory reconstruction problem in which the data are (i) sparsely sampled and (ii) subject to an imperfect observer that introduces noise. Under certain regularity assumptions, we show that the constructed estimator minimizes a specific energy function defined over the trajectory as the number of samples obtained grows.