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Learning
2017.09.04-2017.10.01
难度
60人已参加

简介

The differential entropy plays fundamental roles in the fields of information theory, statistics, machine learning, etc. This project aims at developing a better understanding of how to estimate the differential entropy from empirical data.

工作时间

  • 项目周期:4周
  • 预估每周工作量:8-10小时(均为弹性工作时间)

工作内容

任务1

Week 1

Understand how one could simulate samples from a specific density f. Compute the differential entropy of this density, and implement a sampler that can produce i.i.d. samples from this density.
Notes: The formulas are omitted here, please refer to the attachment of task 1 for details.

任务2

Week 2

Use the JVHW Shannon entropy estimator code on https://github.com/EEthinker/JVHW_Entropy_Estimators to implement this differential entropy estimator. Try to tune the parameter h and plot the root mean squared error for sample sizes n = 102, 103, 104, 105 for the density constructed in Week 1. Report your findings. What h works the best for this density?
Notes: The formulas are omitted here, please refer to the attachment of task 1 for details.

任务3

Week 3

There exist other approaches that directly aim at estimating the differential entropy. One of the most celebrated methods is the so-called nearest neighbor methods. Use the code in https://github.com/liverlover/lnn/blob/master/readme.pdf and compare its performance with the approach in Week 2. Which one works better for the specific density we constructed in Week 1?

任务4

Week 4

Now, construct a smoother density on [0, 1] compared to the one in Week 1, and repeat the experiments in Week 2 and Week 3. Which method now works better? Has anything changed?

工作方式

Team mode, 3 members at most.
Join the QQ group (521929038) after signing up. Some essential information about this project will be published in the group.
Log in to the Qingfan website (http://www.qingfan.com) to check the tasks and upload your submissions.
Project URL: http://www.qingfan.com/project/optimal_estimation_of_the_differential_en...

工作成果评估方法

Peer Review (20%) + Professor Review (80%)

收获

Online Project Experience

All the participants who finish this project will obtain the Qingfan online project experience.

Personal Improvement

Acquire knowledge of differential entropy and develop skills of teamwork, problem solving, information gathering and communication.

Professional Guidance

Outstanding performance will acquire professional guidance of the professor from Stanford University.

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