- #Sequential testing with general loss function trial
- #Sequential testing with general loss function series
Now, we test those new values in the real objective function and not in the surrogate function as in step 3. Selection function: based on the surrogate function evaluations, the selection function will now pick new values for the hyperparameters to test. The surrogate "mimics" the objective function, and it evaluates the current values of the hyperparameters. But we don't use it that much because it's computationally costly and slow, so we use the surrogate. Objective function: this is the function that we want to minimize or maximize (like loss function for example). Nothing special here, excpet that we can refer to this domain as a probability distribution that will change with each iteration (when new data comes along). So there are several steps and factors for this algorithm, I'll talk about them and at the end I'll add a scheme to summarize it, please correct me if I'm wrong:īuild the domain that has the ranges of values that we pick for each hyperparameter. I just want to make sure I understand it right. A Memorandum submitted to the Statistical Research Group, Columbia University, April 1944.One of the hyperparameter tunning approaches that I came across recently is Sequential Model-Based Optimization (SMBO), which is a very smart approach that uses previous iterations in order to find the best values for the hyperparameter. Q.C./R/19.Ībraham Wald, A General Method of Deriving the Operating Characteristics of any Sequential Probability Ratio Test.
#Sequential testing with general loss function series
Stockman, A Method of Obtaining an Approximation for the Operating Characteristic of a Wald Sequential Probability Ratio Test Applied to a Binomial Distribution, (British) Ministry of Supply, Advisory Service on Statistical Method and Quality Control, Technical Report, Series ‘ R’ No. Barnard, M.A., Economy in Sampling with Reference to Engineering Experimentation (British) Ministry of Supply, Advisory Service on Statistical Method and Quality Control, Technical Report, Series ‘ R’ No. A Report submitted by the Statistical Research Group, Columbia University to the Applied Mathematics Panel, National Defense Research Committee, July 1944. Harold Freeman, Sequential Analysis of Statistical Data: Applications. A report submitted by the Statistical Research Group, Columbia University to the Applied Mathematics Panel, National Defense Research Committee, Sept. (1940).Ībraham Wald, Sequential Analysis of Statistical Data: Theory. Conf., Calcutta, Statistical Publishing Soc. Mahalanobis, “A sample survey of the acreage under jute in Bengal, with discussion on planning of experiments,” Proc. Birnbaum, “An inequality for Mill’s ratio”, Annals of Math. 12 (1941).Ībraham Wald, “On cumulative sums of random variables”, Annals of Math. Harold Hotelling, “Experimental determination of the maximum of a function”, Annals of Math. Walter Bartky, “Multiple sampling with constant probability”, Annals of Math. Romig, “A method of sampling inspection,” The Bell System Tech. This process is experimental and the keywords may be updated as the learning algorithm improves. These keywords were added by machine and not by the authors. This process is continued until either the first or the second decision is made.
#Sequential testing with general loss function trial
Again on the basis of the first two trials one of the three decisions is made and if the third decision is reached a third trial is performed, etc. If the third decision is made, a second trial is performed. If the first or the second decision is made, the process is terminated. On the basis of the first trial, one of the three decisions mentioned above is made. Thus, such a test procedure is carried out sequentially. By a sequential test of a statistical hypothesis is meant any statistical test procedure which gives a specific rule, at any stage of the experiment (at the n-th trial for each integral value of n), for making one of the following three decisions: (1) to accept the hypothesis being tested (null hypothesis), (2) to reject the null hypothesis, (3) to continue the experiment by making an additional observation.
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