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Decision trees are one of the most popular classifiers in the machine learning literature. While the most common decision tree learning algorithms treat data as a batch, numerous algorithms have been proposed to construct decision trees…

By adding entropic regularization, multi-marginal optimal transport problems can be transformed into tensor scaling problems, which can be solved numerically using the multi-marginal Sinkhorn algorithm. The main computational bottleneck of…

Maximum Inner Product Search or top-k retrieval on sparse vectors is well-understood in information retrieval, with a number of mature algorithms that solve it exactly. However, all existing algorithms are tailored to text and…

Predicting the evolution of spatiotemporal physical systems from sparse and scattered observational data poses a significant challenge in various scientific domains. Traditional methods rely on dense grid-structured data, limiting their…

The Hadamard decomposition is a powerful technique for data analysis and matrix compression, which decomposes a given matrix into the element-wise product of two or more low-rank matrices. In this paper, we develop an efficient algorithm to…

We present an iterative inverse reinforcement learning algorithm to infer optimal cost functions in continuous spaces. Based on a popular maximum entropy criteria, our approach iteratively finds a weight improvement step and proposes a…

We consider two problems that arise in machine learning applications: the problem of recovering a planted sparse vector in a random linear subspace and the problem of decomposing a random low-rank overcomplete 3-tensor. For both problems,…

The existing machine learning algorithms for minimizing the convex function over a closed convex set suffer from slow convergence because their learning rates must be determined before running them. This paper proposes two machine learning…

The transverse folding algorithm [Phys. Rev. Lett. 102, 240603] is a tensor network method to compute time-dependent local observables in out-of-equilibrium quantum spin chains that can sometimes overcome the limitations of matrix product…

Variational formulations of reconstruction in computed tomography have the notable drawback of requiring repeated evaluations of both the forward Radon transform and either its adjoint or an approximate inverse transform which are…

The growth of big data in domains such as Earth Sciences, Social Networks, Physical Sciences, etc. has lead to an immense need for efficient and scalable linear algebra operations, e.g. Matrix inversion. Existing methods for efficient and…

Optimal transport (OT) naturally arises in a wide range of machine learning applications but may often become the computational bottleneck. Recently, one line of works propose to solve OT approximately by searching the \emph{transport plan}…

Eigenvalue problems have a distinctive forward-inverse structure and are fundamental to characterizing a system's thermal response, stability, and natural modes. Physics-Informed Neural Networks (PINNs) offer a mesh-free alternative for…

Advanced optimization algorithms such as Newton method and AdaGrad benefit from second order derivative or second order statistics to achieve better descent directions and faster convergence rates. At their heart, such algorithms need to…

In this work, we propose a learning method for solving the linear transport equation under the diffusive scaling. Due to the multiscale nature of our model equation, the model is challenging to solve by using conventional methods. We employ…

We consider the problem of detecting a cycle in a directed graph that grows by arc insertions, and the related problems of maintaining a topological order and the strong components of such a graph. For these problems, we give two…

The current best practice for computing optimal transport (OT) is via entropy regularization and Sinkhorn iterations. This algorithm runs in quadratic time as it requires the full pairwise cost matrix, which is prohibitively expensive for…

Optimal transport (OT) distances are finding evermore applications in machine learning and computer vision, but their wide spread use in larger-scale problems is impeded by their high computational cost. In this work we develop a family of…

We propose a differentiable sphere tracing algorithm to bridge the gap between inverse graphics methods and the recently proposed deep learning based implicit signed distance function. Due to the nature of the implicit function, the…

Sequences of linear systems arise in the predictor-corrector method when computing the Pareto front for multi-objective optimization. Rather than discarding information generated when solving one system, it may be advantageous to recycle…