Related papers: On Learning High Dimensional Structured Single Ind…
Single Index Models (SIMs) are simple yet flexible semi-parametric models for classification and regression. Response variables are modeled as a nonlinear, monotonic function of a linear combination of features. Estimation in this context…
Generalized Linear Models (GLMs) and Single Index Models (SIMs) provide powerful generalizations of linear regression, where the target variable is assumed to be a (possibly unknown) 1-dimensional function of a linear predictor. In general,…
Analysis of high-dimensional data has led to increased interest in both single index models (SIMs) and the best-subset selection. SIMs provide an interpretable and flexible modeling framework for high-dimensional data, while the best-subset…
In machine learning and data mining, linear models have been widely used to model the response as parametric linear functions of the predictors. To relax such stringent assumptions made by parametric linear models, additive models consider…
We consider a high-dimensional monotone single index model (hdSIM), which is a semiparametric extension of a high-dimensional generalize linear model (hdGLM), where the link function is unknown, but constrained with monotone and…
Implicit models are a general class of learning models that forgo the hierarchical layer structure typical in neural networks and instead define the internal states based on an ``equilibrium'' equation, offering competitive performance and…
Image registration is an ill-posed dense vision task, where multiple solutions achieve similar loss values, motivating probabilistic inference. Variational inference has previously been employed to capture these distributions, however…
Semiparametric single-index assumptions are convenient and widely used dimen\-sion reduction approaches that represent a compromise between the parametric and fully nonparametric models for regressions or conditional laws. In a mean…
A single-index model (SIM) is a function of the form $\sigma(\mathbf{w}^{\ast} \cdot \mathbf{x})$, where $\sigma: \mathbb{R} \to \mathbb{R}$ is a known link function and $\mathbf{w}^{\ast}$ is a hidden unit vector. We study the task of…
The use of the structural similarity index (SSIM) is widespread. For almost two decades, it has played a major role in image quality assessment in many different research disciplines. Clearly, its merits are indisputable in the research…
Linear mixed models (LMMs) are used extensively to model dependecies of observations in linear regression and are used extensively in many application areas. Parameter estimation for LMMs can be computationally prohibitive on big data.…
Single-index models are a class of functions given by an unknown univariate ``link'' function applied to an unknown one-dimensional projection of the input. These models are particularly relevant in high dimension, when the data might…
Structured illumination microscopy (SIM) is an important super-resolution based microscopy technique that breaks the diffraction limit and enhances optical microscopy systems. With the development of biology and medical engineering, there…
The Structural Similarity (SSIM) Index is a very widely used image/video quality model that continues to play an important role in the perceptual evaluation of compression algorithms, encoding recipes and numerous other image/video…
Network estimation from multi-variate point process or time series data is a problem of fundamental importance. Prior work has focused on parametric approaches that require a known parametric model, which makes estimation procedures less…
Structured illumination microscopy (SIM) improves resolution by down-modulating high-frequency information of an object to fit within the passband of the optical system. Generally, the reconstruction process requires prior knowledge of the…
The problem of statistical inference for regression coefficients in a high-dimensional single-index model is considered. Under elliptical symmetry, the single index model can be reformulated as a proxy linear model whose regression…
In this paper, we aim to estimate the direction of an underlying signal from its nonlinear observations following the semi-parametric single index model (SIM). Unlike conventional compressed sensing where the signal is assumed to be sparse,…
A Distributional (Single) Index Model (DIM) is a semi-parametric model for distributional regression, that is, estimation of conditional distributions given covariates. The method is a combination of classical single index models for the…
We investigate the problem of learning a Single Index Model (SIM)- a popular model for studying the ability of neural networks to learn features - from anisotropic Gaussian inputs by training a neuron using vanilla Stochastic Gradient…