Related papers: List-Decodable Linear Regression
Linear regression is a basic and widely-used methodology in data analysis. It is known that some quantum algorithms efficiently perform least squares linear regression of an exponentially large data set. However, if we obtain values of the…
We study the fundamental problem of fixed design {\em multidimensional segmented regression}: Given noisy samples from a function $f$, promised to be piecewise linear on an unknown set of $k$ rectangles, we want to recover $f$ up to a…
In many learning applications, data are collected from multiple sources, each providing a \emph{batch} of samples that by itself is insufficient to learn its input-output relationship. A common approach assumes that the sources fall in one…
We study the fundamental problem of high-dimensional mean estimation in a robust model where a constant fraction of the samples are adversarially corrupted. Recent work gave the first polynomial time algorithms for this problem with…
We investigate robust linear regression where data may be contaminated by an oblivious adversary, i.e., an adversary than may know the data distribution but is otherwise oblivious to the realizations of the data samples. This model has been…
We propose statistically robust and computationally efficient linear learning methods in the high-dimensional batch setting, where the number of features $d$ may exceed the sample size $n$. We employ, in a generic learning setting, two…
We design a new, fast algorithm for agnostically learning univariate probability distributions whose densities are well approximated by piecewise polynomial functions. Let $f$ be the density function of an arbitrary univariate distribution,…
The task of robust linear estimation in the presence of outliers is of particular importance in signal processing, statistics and machine learning. Although the problem has been stated a few decades ago and solved using classical…
We study the {\em robust proper learning} of univariate log-concave distributions (over continuous and discrete domains). Given a set of samples drawn from an unknown target distribution, we want to compute a log-concave hypothesis…
We use the Sum of Squares method to develop new efficient algorithms for learning well-separated mixtures of Gaussians and robust mean estimation, both in high dimensions, that substantially improve upon the statistical guarantees achieved…
Motivated by the prevalence of environments in which data is abundant while resources for storage and/or transmission might be scarce, we study linear regression when predictors, their squares, and responses are subject to single-bit…
Consider a set $P$ of $n$ points picked uniformly and independently from $[0,1]^d$ for a constant dimension $d$ -- such a point set is extremely well behaved in many aspects. For example, for a fixed $r \in [0,1]$, we prove a new…
Learning from a label distribution has achieved promising results on ordinal regression tasks such as facial age and head pose estimation wherein, the concept of adaptive label distribution learning (ALDL) has drawn lots of attention…
We consider the problem of on-line prediction of real-valued labels, assumed bounded in absolute value by a known constant, of new objects from known labeled objects. The prediction algorithm's performance is measured by the squared…
We give the first polynomial-time algorithm for the testable learning of halfspaces in the presence of adversarial label noise under the Gaussian distribution. In the recently introduced testable learning model, one is required to produce a…
We study the problem of high-dimensional sparse mean estimation in the presence of an $\epsilon$-fraction of adversarial outliers. Prior work obtained sample and computationally efficient algorithms for this task for identity-covariance…
We consider a high dimensional linear regression problem where the goal is to efficiently recover an unknown vector $\beta^*$ from $n$ noisy linear observations $Y=X\beta^*+W \in \mathbb{R}^n$, for known $X \in \mathbb{R}^{n \times p}$ and…
There has been a great deal of work establishing that random linear codes are as list-decodable as uniformly random codes, in the sense that a random linear binary code of rate $1 - H(p) - \epsilon$ is $(p,O(1/\epsilon))$-list-decodable…
We make progress on two important problems regarding attribute efficient learnability. First, we give an algorithm for learning decision lists of length $k$ over $n$ variables using $2^{\tilde{O}(k^{1/3})} \log n$ examples and time…
We consider the problem of sampling from constrained distributions, which has posed significant challenges to both non-asymptotic analysis and algorithmic design. We propose a unified framework, which is inspired by the classical mirror…