Search Results for author: Yi Hao

Found 12 papers, 2 papers with code

TURF: A Two-factor, Universal, Robust, Fast Distribution Learning Algorithm

no code implementations15 Feb 2022 Yi Hao, Ayush Jain, Alon Orlitsky, Vaishakh Ravindrakumar

We derive a near-linear-time and essentially sample-optimal estimator that establishes $c_{t, d}=2$ for all $(t, d)\ne(1, 0)$.

Optimal Prediction of the Number of Unseen Species with Multiplicity

no code implementations NeurIPS 2020 Yi Hao, Ping Li

Based on a sample of size $n$, we consider estimating the number of symbols that appear at least $\mu$ times in an independent sample of size $a \cdot n$, where $a$ is a given parameter.

Unsupervised Embedding of Hierarchical Structure in Euclidean Space

1 code implementation30 Oct 2020 Jinyu Zhao, Yi Hao, Cyrus Rashtchian

To learn the embedding, we revisit using a variational autoencoder with a Gaussian mixture prior, and we show that rescaling the latent space embedding and then applying Ward's linkage-based algorithm leads to improved results for both dendrogram purity and the Moseley-Wang cost function.

SURF: A Simple, Universal, Robust, Fast Distribution Learning Algorithm

no code implementations NeurIPS 2020 Yi Hao, Ayush Jain, Alon Orlitsky, Vaishakh Ravindrakumar

Sample- and computationally-efficient distribution estimation is a fundamental tenet in statistics and machine learning.

Unified Sample-Optimal Property Estimation in Near-Linear Time

no code implementations NeurIPS 2019 Yi Hao, Alon Orlitsky

We consider the fundamental learning problem of estimating properties of distributions over large domains.

The Broad Optimality of Profile Maximum Likelihood

1 code implementation NeurIPS 2019 Yi Hao, Alon Orlitsky

In particular, for every alphabet size $k$ and desired accuracy $\varepsilon$: $\textbf{Distribution estimation}$ Under $\ell_1$ distance, PML yields optimal $\Theta(k/(\varepsilon^2\log k))$ sample complexity for sorted-distribution estimation, and a PML-based estimator empirically outperforms the Good-Turing estimator on the actual distribution; $\textbf{Additive property estimation}$ For a broad class of additive properties, the PML plug-in estimator uses just four times the sample size required by the best estimator to achieve roughly twice its error, with exponentially higher confidence; $\boldsymbol{\alpha}\textbf{-R\'enyi entropy estimation}$ For integer $\alpha>1$, the PML plug-in estimator has optimal $k^{1-1/\alpha}$ sample complexity; for non-integer $\alpha>3/4$, the PML plug-in estimator has sample complexity lower than the state of the art; $\textbf{Identity testing}$ In testing whether an unknown distribution is equal to or at least $\varepsilon$ far from a given distribution in $\ell_1$ distance, a PML-based tester achieves the optimal sample complexity up to logarithmic factors of $k$.

Data Amplification: A Unified and Competitive Approach to Property Estimation

no code implementations NeurIPS 2018 Yi Hao, Alon Orlitsky, Ananda T. Suresh, Yihong Wu

We design the first unified, linear-time, competitive, property estimator that for a wide class of properties and for all underlying distributions uses just $2n$ samples to achieve the performance attained by the empirical estimator with $n\sqrt{\log n}$ samples.

Data Amplification: Instance-Optimal Property Estimation

no code implementations ICML 2020 Yi Hao, Alon Orlitsky

For a large variety of distribution properties including four of the most popular ones and for every underlying distribution, they achieve the accuracy that the empirical-frequency plug-in estimators would attain using a logarithmic-factor more samples.

On Learning Markov Chains

no code implementations NeurIPS 2018 Yi Hao, Alon Orlitsky, Venkatadheeraj Pichapati

We consider two problems related to the min-max risk (expected loss) of estimating an unknown $k$-state Markov chain from its $n$ sequential samples: predicting the conditional distribution of the next sample with respect to the KL-divergence, and estimating the transition matrix with respect to a natural loss induced by KL or a more general $f$-divergence measure.

Maxing and Ranking with Few Assumptions

no code implementations NeurIPS 2017 Moein Falahatgar, Yi Hao, Alon Orlitsky, Venkatadheeraj Pichapati, Vaishakh Ravindrakumar

PAC maximum selection (maxing) and ranking of $n$ elements via random pairwise comparisons have diverse applications and have been studied under many models and assumptions.

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