Clustering Daniel Hsu COMS 4772

COMS 4772 Fall 2013 Mixture models

The mixing distribution is also sometimes called the mixing weights. There are a number of statistical estimation / unsupervised learning tasks associated with mixture models. Three such tasks are as follows (assuming an iid sample from some m? ∈M is given): 1. Density estimation: Here we assume that each distribution in M has a density. The task is to pick m̂ ∈ M such that m̂ is close to m? unde...

COMS 4772 Fall 2014 Experts , bandits , and games

Warning: notes are incomplete and unchecked for correctness 1 Prediction with expert advice Algorithm 1 Protocol for online decision-making with expert advice 1: for t = 1 to T do 2: Receive experts' recommendations: b t,i ∈ {±1} for i ∈ [N ]. Recall that the " Follow the weighted majority " algorithm has the following guarantee. Letting M T denote the number of mistakes made by the learner in ...

Notes for COMS 6998-4 Fall 2017

COMS 4772 Fall 2014

Consider a scenario where you have to repeatedly make a decision on some important matter, and each decision has some quantifiable consequence which you would like to optimize. Formally, suppose there are T rounds of this decision-making game. In each round, you (the “learner”) must choose between two actions, {−1,+1}. Your adversary (Nature) picks one of the actions for that round to be correc...

COMS 6998 - 4 Fall 2017 Presenter : Daniel Hsu

+ errPn(hn)− errPn(h) + errPn(h ∗)− errP (h∗). The second part is less than or equals to 0. We can disregard it when we aim at deriving an upper bound of the regret. Since the target function h∗ is independent of the sample pairs, the third part can be bounded easily by analyzing the binomial distribution with success probability errP (h∗) and n trials. To analyze the remaining first part, we b...