Related papers: SQ Lower Bounds for Learning Mixtures of Linear Cl…
We give the first fully polynomial-time algorithm for learning halfspaces with respect to the uniform distribution on the hypercube in the presence of contamination, where an adversary may corrupt some fraction of examples and labels…
The learning of Gaussian Mixture Models (also referred to simply as GMMs) plays an important role in machine learning. Known for their expressiveness and interpretability, Gaussian mixture models have a wide range of applications, from…
Supervised manifold learning methods learn data representations by preserving the geometric structure of data while enhancing the separation between data samples from different classes. In this work, we propose a theoretical study of…
We consider the problem of learning mixtures of Gaussians under the constraint of approximate differential privacy. We prove that $\widetilde{O}(k^2 d \log^{3/2}(1/\delta) / \alpha^2 \varepsilon)$ samples are sufficient to learn a mixture…
We consider the problem of estimating the error variance in a general linear model when the error distribution is assumed to be spherically symmetric, but not necessary Gaussian. In particular we study the case of a scale mixture of…
In optimization problems, some variable subsets may have a joint non-linear or non-monotonical influence on the function value. Therefore, knowledge of variable dependencies may be crucial for effective optimization, and many…
In unitary property testing a quantum algorithm, also known as a tester, is given query access to a black-box unitary and has to decide whether it satisfies some property. We propose a new technique for proving lower bounds on the quantum…
In this paper, we consider the mixture of sparse linear regressions model. Let ${\beta}^{(1)},\ldots,{\beta}^{(L)}\in\mathbb{C}^n$ be $ L $ unknown sparse parameter vectors with a total of $ K $ non-zero coefficients. Noisy linear…
Discriminative linear models are a popular tool in machine learning. These can be generally divided into two types: The first is linear classifiers, such as support vector machines, which are well studied and provide state-of-the-art…
Consider a regression problem where the learner is given a large collection of $d$-dimensional data points, but can only query a small subset of the real-valued labels. How many queries are needed to obtain a $1+\epsilon$ relative error…
We present a new analysis of the problem of learning with drifting distributions in the batch setting using the notion of discrepancy. We prove learning bounds based on the Rademacher complexity of the hypothesis set and the discrepancy of…
Prior works have shown that semi-supervised learning algorithms can leverage unlabeled data to improve over the labeled sample complexity of supervised learning (SL) algorithms. However, existing theoretical analyses focus on regimes where…
We study a special case of the problem of statistical learning without the i.i.d. assumption. Specifically, we suppose a learning method is presented with a sequence of data points, and required to make a prediction (e.g., a classification)…
In the list-decodable learning setup, an overwhelming majority (say a $1-\beta$-fraction) of the input data consists of outliers and the goal of an algorithm is to output a small list $\mathcal{L}$ of hypotheses such that one of them agrees…
We study the problem of distributed multi-view representation learning. In this problem, $K$ agents observe each one distinct, possibly statistically correlated, view and independently extracts from it a suitable representation in a manner…
In learning theory, a standard assumption is that the data is generated from a finite mixture model. But what happens when the number of components is not known in advance? The problem of estimating the number of components, also called…
We consider the problem of identifying the parameters of an unknown mixture of two arbitrary $d$-dimensional gaussians from a sequence of independent random samples. Our main results are upper and lower bounds giving a computationally…
Gaussian mixture models (GMM) are powerful parametric tools with many applications in machine learning and computer vision. Expectation maximization (EM) is the most popular algorithm for estimating the GMM parameters. However, EM…
Learned index structures aim to accelerate queries by training machine learning models to approximate the rank function associated with a database attribute. While effective in practice, their theoretical limitations are not fully…
This paper proposes a novel Hessian approximation for Maximum a Posteriori estimation problems in robotics involving Gaussian mixture likelihoods. Previous approaches manipulate the Gaussian mixture likelihood into a form that allows the…