Undergraduate students of Columbia College, Barnard College, the School of General Studies, and the School of Engineering and Applied Sciences are invited to apply to the Department of Statistics’ summer internship program.  Students work under the supervision of faculty mentors.  The internship provides a competitive stipend, which includes a summer housing allowance.

Students should send a transcript and a statement of interest that indicates which project or projects they would like to be considered for by email to [email protected].  Students interested in conducting research with Professor Zheng should also complete this form.

Applications will be accepted on a rolling basis, final decisions will be made by April 15, 2026.

For Summer 2026, the following projects are currently available. 

• Professor Allen 
  • Professor Allen can tailor projects in statistical machine learning, unsupervised learning, neuroscience, and genomics to students’ interests and backgrounds.

• Professor Paninski
  • We welcome research assistants to develop and apply new methods for the analysis of neural and behavioral video data.  We are a computational lab collaborating with multiple experimental groups.  Previous experience with Python required; previous experience with machine learning would be helpful.  For some recent projects, see here.

• Professor Zheng
  • Professor Tian Zheng offers research opportunities in her TZstats Convergence Lab that focus on developing and evaluating modern statistical and machine-learning methods for analyzing complex urban and socio-technical data. Students will work on projects that may include Bayesian modeling to correct reporting biases in large-scale civic data (e.g., 311 complaints), studying spatial reasoning and representation learning in vision transformers, developing simulation-based inference workflows for urban flooding models, or systematically evaluating generative AI tools for data analysis and scientific reasoning. Across projects, students will gain experience in probabilistic modeling, deep learning, and computational experimentation, with an emphasis on reproducibility, uncertainty quantification, and the integration of domain knowledge into data-driven models. Strong programming skills in Python are required; familiarity with Bayesian methods, PyTorch, applied mathematics, or machine learning is beneficial depending on project focus.

• Professor Dube
  • Time Series Foundation Models for Causal Discovery in Nonlinear Dynamic Systems. This project proposes to explore the integration of Time Series Foundation Models (TSFMs) [1] with Empirical Dynamic Modeling (EDM) [2] as a novel framework for analyzing complex dynamical systems that evade traditional causal inference and forecasting approaches. TSFMs, as large-scale, self-supervised neural models pretrained on diverse temporal corpora, have demonstrated the capacity to capture long-range dependencies, regime shifts, and latent structure in sequential data, offering broad generalization and flexible representation learning. Meanwhile, EDM provides a data-driven, model-free approach rooted in dynamic systems theory for reconstructing system attractors from time series, characterizing system complexity & nonlinearity (e.g., through simplex projection and S-maps), and identifying causal interactions via convergent cross mapping without assuming linearity, stability, or equilibrium — addressing fundamental limitations of classic experimental or regression-based methods in nonlinear domains. EDM’s foundational logic shows that dynamic attractors can be reconstructed from observed time series (Takens’ embedding) and that causal influence can be distinguished from mere correlation even under mirage correlations that confound linear analysis . TSFMs offer complementary advantages by learning rich temporal representations that could enhance state-space reconstructions and facilitate scalable causal discovery and predictive modeling in high-dimensional, noisy real-world systems. The research objective is to evaluate whether and how TSFMs can serve as function approximators or embedding enhancers within the EDM framework, improving nonlinear forecasting accuracy and causal inference robustness while preserving EDM’s minimal assumption paradigm, thereby advancing tools for studying complex phenomena in ecology, climate, economics, and beyond. [1] IBM Granite TimeSeries TTM [2] Detecting causality in complex ecosystems

• • When Machines Socialize: Measuring World Models and Alignment in Autonomous AI Societies. This study proposes an empirical and theoretical study of representational alignment among AI agents operating within autonomous social-media ecosystems such as OpenClaw platform — a recently documented network where AI agents engage with one another, sometimes producing emergent behaviors traditionally associated with collective cognition and self-referential discourse (e.g., religion-like discussions among bots) . Drawing on the framework articulated in Nature Computational Science that leverages large language models to advance understanding of collective cognition and the complexity of shared information spaces , this study aims to quantify how distinct agents represent states of the external and social environment, measure convergence or divergence in their internal world models, and assess how their latent representations align or misalign both with each other and with human interpretive frameworks. The research will build on recent work in quantifying world models and representational geometry across AI systems, integrating metrics from cognitive science and machine learning to operationalize alignment (e.g., representational overlap, predictive consistency) and combining this with behavioral analysis of multi-agent interaction patterns. [1] OpenClaw AI chatbots are running amok — these scientists are listening in [2] Using LLMs to advance the cognitive science of collectives [3] OpenClaw

• Professor Maleki
  • Modern imaging systems such as MRI, CT, electron microscopy, and holography do not directly capture images in the way a camera does. Instead, they collect indirect measurements, for example, frequency samples in MRI, line integrals in CT, or interference patterns in holography, that must be mathematically transformed into a visual image. This process is known as an inverse problem, and it is often ill-posed: the measurements may be noisy, incomplete, or limited by physical constraints such as scan time, radiation dose, or instrument resolution. Traditional reconstruction methods rely on carefully designed physical models and optimization techniques, which can work well but often struggle when data are extremely sparse, corrupted, or collected under strict practical limitations. Recent advances in modern AI, especially deep generative models and foundation models for vision, offer a new paradigm for image reconstruction. These models can learn rich structural priors from large datasets and use them to fill in missing information or denoise measurements in ways that classical methods cannot. In this project, we aim to develop AI-driven reconstruction methods that integrate physical measurement models with modern generative techniques, enabling accurate recovery of images from limited or noisy data across applications such as MRI, CT, electron microscopy, and holography. The goal is to design algorithms that are both computationally efficient and statistically robust, pushing the limits of what can be reconstructed under real-world constraints.

• Professor Haiyuan Wang
  • A Unified Digital Ecosystem for Automotive & Insurance Stakeholders.   The primary objective of this initiative is to design and develop a sophisticated digital platform—or a suite of interconnected applications—that serves as a central nexus for the automotive aftermarket ecosystem.  
  • Predicting equity futures market prices using machine learning.  This research project leverages sophisticated algorithms and large datasets to identify patterns, forecast price movements, and guide trading strategies for equity futures.
  • See here for more details.