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Found 19 papers, 2 papers with code
Sample-Efficient Private Learning of Mixtures of Gaussians
We study the problem of learning mixtures of Gaussians with approximate differential privacy.
Agnostic Private Density Estimation for GMMs via List Global Stability
We consider the problem of private density estimation for mixtures of unrestricted high dimensional Gaussians in the agnostic setting.
Sample-Optimal Locally Private Hypothesis Selection and the Provable Benefits of Interactivity
Namely, it breaks the known lower bound of $\Omega\left(\frac{k\log k}{\alpha^2\min \{ \varepsilon^2 , 1\}} \right)$ for the sample complexity of non-interactive hypothesis selection.
Mixtures of Gaussians are Privately Learnable with a Polynomial Number of Samples
We study the problem of estimating mixtures of Gaussians under the constraint of differential privacy (DP).
Polynomial Time and Private Learning of Unbounded Gaussian Mixture Models
We study the problem of privately estimating the parameters of $d$-dimensional Gaussian Mixture Models (GMMs) with $k$ components.
Benefits of Additive Noise in Composing Classes with Bounded Capacity
We observe that given two (compatible) classes of functions $\mathcal{F}$ and $\mathcal{H}$ with small capacity as measured by their uniform covering numbers, the capacity of the composition class $\mathcal{H} \circ \mathcal{F}$ can become prohibitively large or even unbounded.
Adversarially Robust Learning with Tolerance
In the tolerant version, the error of the learner is compared with the best achievable error with respect to a slightly larger perturbation radius $(1+\gamma)r$.
Private and polynomial time algorithms for learning Gaussians and beyond
As another application of our framework, we provide the first polynomial time $(\varepsilon, \delta)$-DP algorithm for robust learning of (unrestricted) Gaussians with sample complexity $\widetilde{O}(d^{3. 5})$.
Privately Learning Mixtures of Axis-Aligned Gaussians
We show that if $\mathcal{F}$ is privately list-decodable, then we can privately learn mixtures of distributions in $\mathcal{F}$.
On the Sample Complexity of Privately Learning Unbounded High-Dimensional Gaussians
These are the first finite sample upper bounds for general Gaussians which do not impose restrictions on the parameters of the distribution.
Black-box Certification and Learning under Adversarial Perturbations
We formally study the problem of classification under adversarial perturbations from a learner's perspective as well as a third-party who aims at certifying the robustness of a given black-box classifier.
On the Sample Complexity of Learning Sum-Product Networks
We show that the sample complexity of learning tree structured SPNs with the usual type of leaves (i. e., Gaussian or discrete) grows at most linearly (up to logarithmic factors) with the number of parameters of the SPN.
Disentangled behavioural representations
Individual characteristics in human decision-making are often quantified by fitting a parametric cognitive model to subjects' behavior and then studying differences between them in the associated parameter space.
Nearly tight sample complexity bounds for learning mixtures of Gaussians via sample compression schemes
We prove that ϴ(k d^2 / ε^2) samples are necessary and sufficient for learning a mixture of k Gaussians in R^d, up to error ε in total variation distance.
Some techniques in density estimation
Density estimation is an interdisciplinary topic at the intersection of statistics, theoretical computer science and machine learning.
Near-optimal Sample Complexity Bounds for Robust Learning of Gaussians Mixtures via Compression Schemes
We prove that $\tilde{\Theta}(k d^2 / \varepsilon^2)$ samples are necessary and sufficient for learning a mixture of $k$ Gaussians in $\mathbb{R}^d$, up to error $\varepsilon$ in total variation distance.
Sample-Efficient Learning of Mixtures
Let $\mathcal F$ be an arbitrary class of probability distributions, and let $\mathcal{F}^k$ denote the class of $k$-mixtures of elements of $\mathcal F$.
Clustering with Same-Cluster Queries
We show that there is a trade off between computational complexity and query complexity; We prove that for the case of $k$-means clustering (i. e., when the expert conforms to a solution of $k$-means), having access to relatively few such queries allows efficient solutions to otherwise NP hard problems.
Representation Learning for Clustering: A Statistical Framework
The algorithm designer then uses that sample to come up with a data representation under which $k$-means clustering results in a clustering (of the full data set) that is aligned with the user's clustering.
