Related papers: Blind Polynomial Regression
Simple function classes have emerged as toy problems to better understand in-context-learning in transformer-based architectures used for large language models. But previously proposed simple function classes like linear regression or…
In some multivariate problems with missing data, pairs of variables exist that are never observed together. For example, some modern biological tools can produce data of this form. As a result of this structure, the covariance matrix is…
We address the problem of approximating an unknown function from its discrete samples given at arbitrarily scattered sites. This problem is essential in numerical sciences, where modern applications also highlight the need for a solution to…
Blind Perspective-n-Point (PnP) is the problem of estimating the position and orientation of a camera relative to a scene, given 2D image points and 3D scene points, without prior knowledge of the 2D-3D correspondences. Solving for pose and…
In ill-posed imaging inverse problems, uncertainty quantification remains a fundamental challenge, especially in safety-critical applications. Recently, conformal prediction has been used to quantify the uncertainty that the inverse problem…
Deconvolution is a fundamental inverse problem in signal processing and the prototypical model for recovering a signal from its noisy measurement. Nevertheless, the majority of model-based inversion techniques require knowledge on the…
This work provides a complete characterization of the solutions of a linear interpolation problem for vector polynomials. The interpolation problem consists in finding n scalar polynomials such that an equation involving a linear…
Human inertial thinking schemes can be formed through learning, which are then applied to quickly solve similar problems later. However, when problems are significantly different, inertial thinking generally presents the solutions that are…
We consider the problem of recovering linear image of unknown signal belonging to a given convex compact signal set from noisy observation of another linear image of the signal. We develop a simple generic efficiently computable nonlinear…
We discuss a technique that allows blind recovery of signals or blind identification of mixtures in instances where such recovery or identification were previously thought to be impossible: (i) closely located or highly correlated sources…
As a popular and easy-to-implement machine learning method for solving differential equations, the physics-informed neural network (PINN) sometimes may fail and find poor solutions which bias against the exact ones. In this paper, we…
In many physical systems, inputs related by intrinsic system symmetries are mapped to the same output. When inverting such systems, i.e., solving the associated inverse problems, there is no unique solution. This causes fundamental…
Twinned regression methods are designed to solve the dual problem to the original regression problem, predicting differences between regression targets rather then the targets themselves. A solution to the original regression problem can be…
When using images to locate objects, there is the problem of correcting for distortion and misalignment in the images. An elegant way of solving this problem is to generate an error correcting function that maps points in an image to their…
This paper studies the problem of multivariate linear regression where a portion of the observations is grossly corrupted or is missing, and the magnitudes and locations of such occurrences are unknown in priori. To deal with this problem,…
This paper provides partial identification of various binary choice models with misreported dependent variables. We propose two distinct approaches by exploiting different instrumental variables respectively. In the first approach, the…
Finite linear least squares is one of the core problems of numerical linear algebra, with countless applications across science and engineering. Consequently, there is a rich and ongoing literature on algorithms for solving linear least…
We study Matching and other related problems in a partial information setting where the agents' utilities for being matched to other agents are hidden and the mechanism only has access to ordinal preference information. Our model is…
We consider the problem of reconstructing two signals from the autocorrelation and cross-correlation measurements. This inverse problem is a fundamental one in signal processing, and arises in many applications, including phase retrieval…
Data analysis based on information from several sources is common in economic and biomedical studies. This setting is often referred to as the data fusion problem, which differs from traditional missing data problems since no complete data…