# Testing Properties of Multiple Distributions with Few Samples

Sandeep Silwal

ITCS, 2020.

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Abstract:

We propose a new setting for testing properties of distributions while receiving samples from several distributions, but few samples per distribution. Given samples from $s$ distributions, $p_1, p_2, \ldots, p_s$, we design testers for the following problems: (1) Uniformity Testing: Testing whether all the $p_i #x27;s are uniform or$\epsil...More

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s are uniform or $\\epsilon$-far from being uniform in $\\ell_1$-distance (2) Identity Testing: Testing whether all the $p_i s are equal to an explicitly given distribution$q$or$\\epsilon$-far from$q$in$\\ell_1$-distance, and (3) Closeness Testing: Testing whether all the$p_i s are equal to a distribution $q$ which we have sample access to, or $\\epsilon$-far from $q$ in $\\ell_1$-distance. By assuming an additional natural condition about the source distributions, we provide sample optimal testers for all of these problems. ","authors":[{"id":"5626eb9545ce1e596566babb","name":"Maryam Aliakbarpour"},{"name":"Sandeep Silwal"}],"doi":"10.4230\u002FLIPIcs.ITCS.2020.69","flags":[{"flag":"affirm_author","person_id":"5626eb9545ce1e596566babb"}],"id":"5e15adcc3a55ac47ab5b0be3","is_downvoted":false,"is_starring":false,"is_upvoted":false,"num_citation":0,"num_starred":0,"num_upvoted":0,"num_viewed":3,"pdf":"https:\u002F\u002Fstatic.aminer.cn\u002Fstorage\u002Fpdf\u002Farxiv\u002F19\u002F1911\u002F1911.07324.pdf","title":"Testing Properties of Multiple Distributions with Few Samples.","urls":["https:\u002F\u002Fdblp.org\u002Frec\u002Fconf\u002Finnovations\u002FAliakbarpourS20","https:\u002F\u002Fdoi.org\u002F10.4230\u002FLIPIcs.ITCS.2020.69","https:\u002F\u002Farxiv.org\u002Fabs\u002F1911.07324"],"venue":{"info":{"name":"ITCS"}},"versions":[{"id":"5e15adcc3a55ac47ab5b0be3","sid":"conf\u002Finnovations\u002FAliakbarpourS20","src":"dblp","vsid":"conf\u002Finnovations","year":2020},{"id":"5dd3bf513a55ac1bdd46d8a1","sid":"1911.07324","src":"arxiv","year":2019}],"year":2020,"cited_pubs":0,"total_ref":0,"total_sim":0},"bestpaper":undefined,"simpapers":undefined,"authorsData":[{"avatar":"https:\u002F\u002Fstatic.aminer.cn\u002Fupload\u002Favatar\u002F53\u002F607\u002F67\u002F5626eb9545ce1e596566babb_0.jpg","id":"5626eb9545ce1e596566babb","name":"Maryam Aliakbarpour"},{"name":"Sandeep Silwal"}],"redirect_id":undefined,"notfound":undefined,"pdfInfo":{}};