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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Local case-control sampling ： ウィキペディア英語版 Local case-control sampling In machine learning, local case-control sampling is an algorithm used to reduce the complexity of training a logistic regression classifier. The algorithm reduces the training complexity by selecting a small subsample of the original dataset for training. It assumes the availability of a (unreliable) pilot estimation of the parameters. It then performs a single pass over the entire dataset using the pilot estimation to identify the most "surprising" samples. In practice, the pilot may come from prior knowledge or training using a subsample of the dataset. The algorithm is most effective when the underlying dataset is imbalanced. It exploits the structures of conditional imbalanced datasets more efficiently than alternative methods, such as case control sampling and weighted case control sampling. == Imbalanced datasets == In classification, a dataset is a set of ''N'' data points $(x\_i,\; y\_i)\_^N$, where $x\_i\; \backslash in\backslash mathbb\; R^d$ is a feature vector, $y\_i\; \backslash in\; \backslash$ is a label. Intuitively, a dataset is imbalanced when certain important statistical patterns are rare. The lack of observations of certain patterns does not always imply their irrelevance. For example, in medical studies of rare diseases, the small number of infected patients (cases) conveys the most valuable information for diagnosis and treatments. Formally, an imbalanced dataset exhibits one or more of the following properties: * ''Marginal Imbalance''. A dataset is marginally imbalanced if one class is rare compared to the other class. In other words, $\backslash mathbb(Y=1)\; \backslash approx\; 0$. * ''Conditional Imbalance''. A dataset is conditionally imbalanced when it is easy to predict the correct labels in most cases. For example, if $X\; \backslash in\; \backslash$, the dataset is conditionally imbalanced if $\backslash mathbb(Y=1\backslash mid\; X=0)\; \backslash approx\; 0$ and $\backslash mathbb(Y=1\backslash mid\; X=1)\; \backslash approx\; 1$. == Algorithm outline == In logistic regression, given the model $\backslash theta\; =\; (\backslash alpha,\; \backslash beta)$, the prediction is made according to $\backslash mathbb(Y=1\backslash mid\; X;\; \backslash theta)\; =\; \backslash tilde\_(x)\; =\; \backslash frac$. The local-case control sampling algorithm assumes the availability of a pilot model $\backslash tilde\; =\; (\backslash tilde,\; \backslash tilde)$. Given the pilot model, the algorithm performs a single pass over the entire dataset to select the subset of samples to include in training the logistic regression model. For a sample $(x,y)$, define the acceptance probability as $a(x,y)\; =\; |y-\backslash tilde\_(a(x\_i,y\_i))$ for $i\; \backslash in\; \backslash$. # Fit a logistic regression model to the subsample $S\; =\; \backslash$, obtaining the unadjusted estimates $\backslash hat\_S\; =\; (\backslash hat\_S,\; \backslash hat\_S)$. # The output model is $\backslash hat\; =\; (\backslash hat,\; \backslash hat)$, where $\backslash hat\; \backslash leftarrow\; \backslash hat\_S\; +\; \backslash tilde$ and $\backslash hat\; \backslash leftarrow\; \backslash hat\_S\; +\; \backslash tilde$. The algorithm can be understood as selecting samples that surprises the pilot model. Intuitively these samples are closer to the decision boundary of the classifier and is thus more informative. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Local case-control sampling」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.