
ListDecodable Linear Regression
We give the first polynomialtime algorithm for robust regression in the...
read it

Statistical Query Lower Bounds for ListDecodable Linear Regression
We study the problem of listdecodable linear regression, where an adver...
read it

Efficient Algorithms for OutlierRobust Regression
We give the first polynomialtime algorithm for performing linear or pol...
read it

ListDecodable Subspace Recovery via SumofSquares
We give the first efficient algorithm for the problem of listdecodable ...
read it

Correcting the bias in least squares regression with volumerescaled sampling
Consider linear regression where the examples are generated by an unknow...
read it

Robust Metalearning for Mixed Linear Regression with Small Batches
A common challenge faced in practical supervised learning, such as medic...
read it

Conditional Linear Regression
Work in machine learning and statistics commonly focuses on building mod...
read it
List Decodable Learning via Sum of Squares
In the listdecodable learning setup, an overwhelming majority (say a 1βfraction) of the input data consists of outliers and the goal of an algorithm is to output a small list L of hypotheses such that one of them agrees with inliers. We develop a framework for listdecodable learning via the SumofSquares SDP hierarchy and demonstrate it on two basic statistical estimation problems Linear regression: Suppose we are given labelled examples {(X_i,y_i)}_i ∈ [N] containing a subset S of β N inliers {X_i }_i ∈ S that are drawn i.i.d. from standard Gaussian distribution N(0,I) in R^d, where the corresponding labels y_i are wellapproximated by a linear function ℓ. We devise an algorithm that outputs a list L of linear functions such that there exists some ℓ̂∈L that is close to ℓ. This yields the first algorithm for linear regression in a listdecodable setting. Our results hold for any distribution of examples whose concentration and anticoncentration can be certified by SumofSquares proofs. Mean Estimation: Given data points {X_i}_i ∈ [N] containing a subset S of β N inliers {X_i }_i ∈ S that are drawn i.i.d. from a Gaussian distribution N(μ,I) in R^d, we devise an algorithm that generates a list L of means such that there exists μ̂∈L close to μ. The recovery guarantees of the algorithm are analogous to the existing algorithms for the problem by Diakonikolas and Kothari . In an independent and concurrent work, Karmalkar KlivansKS19 also obtain an algorithm for listdecodable linear regression using the SumofSquares SDP hierarchy.
READ FULL TEXT
Comments
There are no comments yet.