4 papers
Learning Arithmetic Formulas in the Presence of Noise: A General Framework and Applications to Unsupervised Learning
Pritam Chandra, Ankit Garg, Neeraj Kayal +2
We present a general framework for designing efficient algorithms for unsupervised learning problems, such as mixtures of Gaussians and subspace clustering. Our framework is based…
Low-depth arithmetic circuit lower bounds via shifted partials
Prashanth Amireddy, Ankit Garg, Neeraj Kayal +2
We prove super-polynomial lower bounds for low-depth arithmetic circuits using the shifted partials measure [Gupta-Kamath-Kayal-Saptharishi, CCC 2013], [Kayal, ECCC 2012] and the a…
Learning sums of powers of low-degree polynomials in the non-degenerate case
Ankit Garg, Neeraj Kayal, Chandan Saha
We develop algorithms for writing a polynomial as sums of powers of low degree polynomials. Consider an -variate degree- polynomial which can be written as $$f = c_1Q_1^{…
Square root Bound on the Least Power Non-residue using a Sylvester-Vandermonde Determinant
Michael Forbes, Neeraj Kayal, Rajat Mittal +1
We give a new elementary proof of the fact that the value of the least power non-residue in an arithmetic progression , over a prime field $\F_p$, is…