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• Waiting:Sample Problem
  206 bytes (36 words) - 20:45, 16 September 2021

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• Bibliography
  .... ''Laminar Families and Metric Embeddings: Non-bipartite Maximum Matching Problem in the Semi-Streaming Model.'' In ''CoRR,'' abs/1104.4058, 2011.}} ...n randomized streaming space bounds for the longest increasing subsequence problem.'' Electronic Colloquium on Computational Complexity (ECCC), 10(10), 2010.}
  45 KB (5,687 words) - 02:01, 13 March 2023
• Waiting
  Submitting a new problem: # Make sure your problem is not yet on [[Open_Problems:By_Number|the list]].
  704 bytes (113 words) - 17:33, 11 September 2023
• Template:ProblemName
  | 85 = Sample Stretching | !!! ADD THE PROBLEM NAME TO Template:ProblemName !!!
  4 KB (463 words) - 18:05, 26 August 2019
• Open Problems:66
  ...$p_j$ is the probability of drawing an element $j$ from $P$, a conditional sample from $P$ restricted to $S$ is drawn from the distribution where It is known that if one of the distributions is fixed, then the testing problem requires at most $\tilde O(1/\epsilon^4)$ queries, which is independent of
  2 KB (330 words) - 19:20, 7 November 2018
• Open Problems:81
  ...nes for every non-integer $\alpha \geq 0$. In the later case, however, the sample complexity is only known up to a subpolynomial factor: resolving the exact
  877 bytes (148 words) - 06:04, 8 November 2017
• Open Problems:82
  ...$ and (ii) $\operatorname{d}_{\rm TV}(p,q)>\varepsilon$. (The ''identity'' problem is the analogue when $q$ is fixed and explicitly known beforehand.) ...s of Valiant and Valiant {{cite|ValiantV-11}} imply that this question has sample complexity $\Theta\left(\frac{n}{\varepsilon^2\log n}\right)$.
  2 KB (269 words) - 06:10, 8 November 2017
• Open Problems:83
  ...$[n]$ and distance parameter $\varepsilon\in(0,1]$, the identity testing problem asks to distinguish w.h.p. between (i) $p=q$ and (ii) $\operatorname{d}_{\r ...iantV-14}} shown an ''instance-specific'' bound on this problem, where the sample complexity $\Psi_{\rm TV}$ now only depends on $\varepsilon$ and the (massi
  3 KB (437 words) - 14:54, 8 November 2017
• Open Problems:89
  ...computation (as abstracted in the infamous $\mathsf{P}$ vs. $\mathsf{NP}$ problem), the hope is that using the aid of a proof, or a prover, distribution test ...a property $\mathcal{P}$ of distributions over domain $\Omega$ is given ''sample'' access to a distribution $D$ and ''explicit'' access to a proof $\pi$. Gi
  2 KB (305 words) - 16:11, 8 November 2017
• Open Problems:86
  ...g'' (and ''instance-specific'' identity testing — see [[Open_Problems:83|Problem 83]]). Recall that the ''equivalence'' testing problem (also known as closeness testing) is the generalization of identity testing
  1 KB (170 words) - 15:56, 8 November 2017
• Open Problems:87
  (This is a continuation of [[Open_Problems:66|Problem 66]] from the [[Workshops:Bertinoro_2014|2014 Bertinoro Workshop on Subline For constant $\varepsilon>0$, it is known that the sample complexity of equivalence testing, in the conditional oracle model where th
  648 bytes (93 words) - 16:05, 8 November 2017
• Open Problems:96
  ...utations, to test “identity up to relabeling” (a problem whose sample complexity is, from previous work of Valiant and Valiant, known to be $\The ...ily of all partitions of $[n]$ into $m$ consecutive intervals, what is the sample complexity of $\mathcal{F}$-identity testing, as a function of $n$, $\vare
  2 KB (297 words) - 18:12, 26 August 2019
• Open Problems talk:85
  ...t would be worth looking at whether their methods imply a solution to this problem. At the very least, it is very relevant. [1] Sample Amplification:Increasing Dataset Size even when Learning is Impossible; Bri
  442 bytes (70 words) - 08:55, 12 April 2021
• Waiting:Sample Complexity for Streaming Multi-Armed Bandit and Coin Tossing
  |title=Sample Complexity for Streaming Multi-Armed Bandit and Coin Tossing ...ases, find the most biased coin using 1). a minimal number of coin tosses (sample complexity) and 2). a small number of stored coins at any point of the stre
  4 KB (630 words) - 22:13, 25 November 2021