Alex Gorodetsky

Joshua Pickard, Ram Prakash, Marc Andrew Choi et al.

Recent advancements in Large Language Models (LLMs) are transforming biology, computer science, engineering, and every day life. However, integrating the wide array of computational tools, databases, and scientific literature continues to pose a challenge to biological research. LLMs are well-suited for unstructured integration, efficient information retrieval, and automating standard workflows and actions from these diverse resources. To harness these capabilities in bioinformatics, we present a prototype Bioinformatics Retrieval Augmented Digital assistant (BRAD). BRAD is a chatbot and agentic system that integrates a variety of bioinformatics tools. The Python package implements an AI \texttt{Agent} that is powered by LLMs and connects to a local file system, online databases, and a user's software. The \texttt{Agent} is highly configurable, enabling tasks such as Retrieval-Augmented Generation, searches across bioinformatics databases, and the execution of software pipelines. BRAD's coordinated integration of bioinformatics tools delivers a context-aware and semi-autonomous system that extends beyond the capabilities of conventional LLM-based chatbots. A graphical user interface (GUI) provides an intuitive interface to the system.

Zheng Guo, Aditya Deshpande, Brian Kiedrowski et al.

Tensor networks provide a powerful framework for compressing multi-dimensional data. The optimal tensor network structure for a given data tensor depends on both data characteristics and specific optimality criteria, making tensor network structure search a difficult problem. Existing solutions typically rely on sampling and compressing numerous candidate structures; these procedures are computationally expensive and therefore limiting for practical applications. We address this challenge by viewing tensor network structure search as a program synthesis problem and introducing an efficient constraint-based assessment method that avoids costly tensor decomposition. Specifically, we establish a correspondence between transformation programs and network structures. We also design a novel operation named output-directed splits to reduce the search space without hindering expressiveness. We then propose a synthesis algorithm to identify promising network candidates through constraint solving, and avoid tensor decomposition for all but the most promising candidates. Experimental results show that our approach improves search speed by up to $10\times$ and achieves compression ratios $1.5\times$ to $3\times$ better than state-of-the-art. Notably, our approach scales to larger tensors that are unattainable by prior work. Furthermore, the discovered topologies generalize well to similar data, yielding compression ratios up to $ 2.4\times$ better than a generic structure while the runtime remains around $110$ seconds.

Tiangang Cui, Alex Gorodetsky

We present a new sampling-based approach for enabling efficient computation of low-rank Bayesian matrix completion and quantifying the associated uncertainty. Firstly, we design a new prior model based on the singular-value-decomposition (SVD) parametrization of low-rank matrices. Our prior is analogous to the seminal nuclear-norm regularization used in non-Bayesian setting and enforces orthogonality in the factor matrices by constraining them to Stiefel manifolds. Then, we design a geodesic Hamiltonian Monte Carlo (-within-Gibbs) algorithm for generating posterior samples of the SVD factor matrices. We demonstrate that our approach resolves the sampling difficulties encountered by standard Gibbs samplers for the common two-matrix factorization used in matrix completion. More importantly, the geodesic Hamiltonian sampler allows for sampling in cases with more general likelihoods than the typical Gaussian likelihood and Gaussian prior assumptions adopted in most of the existing Bayesian matrix completion literature. We demonstrate an applications of our approach to fit the categorical data of a mice protein dataset and the MovieLens recommendation problem. Numerical examples demonstrate superior sampling performance, including better mixing and faster convergence to a stationary distribution. Moreover, they demonstrate improved accuracy on the two real-world benchmark problems we considered.

Alex Gorodetsky, John D. Jakeman, Gianluca Geraci

We present an approach for constructing a surrogate from ensembles of information sources of varying cost and accuracy. The multifidelity surrogate encodes connections between information sources as a directed acyclic graph, and is trained via gradient-based minimization of a nonlinear least squares objective. While the vast majority of state-of-the-art assumes hierarchical connections between information sources, our approach works with flexibly structured information sources that may not admit a strict hierarchy. The formulation has two advantages: (1) increased data efficiency due to parsimonious multifidelity networks that can be tailored to the application; and (2) no constraints on the training data -- we can combine noisy, non-nested evaluations of the information sources. Numerical examples ranging from synthetic to physics-based computational mechanics simulations indicate the error in our approach can be orders-of-magnitude smaller, particularly in the low-data regime, than single-fidelity and hierarchical multifidelity approaches.

Saibal De, Hadi Salehi, Alex Gorodetsky

Bayesian low-rank matrix factorization techniques have become an essential tool for relational data analysis and matrix completion. A standard approach is to assign zero-mean Gaussian priors on the columns or rows of factor matrices to create a conjugate system. This choice of prior leads to simple implementations; however it also causes symmetries in the posterior distribution that can severely reduce the efficiency of Markov-chain Monte-Carlo (MCMC) sampling approaches. In this paper, we propose a simple modification to the prior choice that provably breaks these symmetries and maintains/improves accuracy. Specifically, we provide conditions that the Gaussian prior mean and covariance must satisfy so the posterior does not exhibit invariances that yield sampling difficulties. For example, we show that using non-zero linearly independent prior means significantly lowers the autocorrelation of MCMC samples, and can also lead to lower reconstruction errors.

Nicholas Galioto, Alex Gorodetsky

We evaluate the robustness of a probabilistic formulation of system identification (ID) to sparse, noisy, and indirect data. Specifically, we compare estimators of future system behavior derived from the Bayesian posterior of a learning problem to several commonly used least squares-based optimization objectives used in system ID. Our comparisons indicate that the log posterior has improved geometric properties compared with the objective function surfaces of traditional methods that include differentially constrained least squares and least squares reconstructions of discrete time steppers like dynamic mode decomposition (DMD). These properties allow it to be both more sensitive to new data and less affected by multiple minima --- overall yielding a more robust approach. Our theoretical results indicate that least squares and regularized least squares methods like dynamic mode decomposition and sparse identification of nonlinear dynamics (SINDy) can be derived from the probabilistic formulation by assuming noiseless measurements. We also analyze the computational complexity of a Gaussian filter-based approximate marginal Markov Chain Monte Carlo scheme that we use to obtain the Bayesian posterior for both linear and nonlinear problems. We then empirically demonstrate that obtaining the marginal posterior of the parameter dynamics and making predictions by extracting optimal estimators (e.g., mean, median, mode) yields orders of magnitude improvement over the aforementioned approaches. We attribute this performance to the fact that the Bayesian approach captures parameter, model, and measurement uncertainties, whereas the other methods typically neglect at least one type of uncertainty.