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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 empirical risk minimization ： ウィキペディア英語版 empirical risk minimization Empirical risk minimization (ERM) is a principle in statistical learning theory which defines a family of learning algorithms and is used to give theoretical bounds on the performance of learning algorithms. == Background == Consider the following situation, which is a general setting of many supervised learning problems. We have two spaces of objects $X$ and $Y$ and would like to learn a function $\backslash !\; h:\; X\; \backslash to\; Y$ (often called ''hypothesis'') which outputs an object $y\; \backslash in\; Y$, given $x\; \backslash in\; X$. To do so, we have at our disposal a ''training set'' of a few examples $\backslash !\; (x\_1,\; y\_1),\; \backslash ldots,\; (x\_m,\; y\_m)$ where $x\_i\; \backslash in\; X$ is an input and $y\_i\; \backslash in\; Y$ is the corresponding response that we wish to get from $\backslash !\; h(x\_i)$. To put it more formally, we assume that there is a joint probability distribution $P(x,\; y)$ over $X$ and $Y$, and that the training set consists of $m$ instances $\backslash !\; (x\_1,\; y\_1),\; \backslash ldots,\; (x\_m,\; y\_m)$ drawn i.i.d. from $P(x,\; y)$. Note that the assumption of a joint probability distribution allows us to model uncertainty in predictions (e.g. from noise in data) because $y$ is not a deterministic function of $x$, but rather a random variable with conditional distribution $P(y\; |\; x)$ for a fixed $x$. We also assume that we are given a non-negative real-valued loss function $L(\backslash hat,\; y)$ which measures how different the prediction $\backslash hat$ of a hypothesis is from the true outcome $y$. The risk associated with hypothesis $h(x)$ is then defined as the expectation of the loss function: : $R(h)\; =\; \backslash mathbf(y))\; =\; \backslash int\; L(h(x),\; y)\backslash ,dP(x,\; y).$ A loss function commonly used in theory is the 0-1 loss function: $L(\backslash hat,\; y)\; =\; I(\backslash hat\; \backslash ne\; y)$, where $I(...)$ is the indicator notation. The ultimate goal of a learning algorithm is to find a hypothesis $h^$ * among a fixed class of functions $\backslash mathcal$ for which the risk $R(h)$ is minimal: : $h^$ * = \arg \min_{h \in \mathcal{H}} R(h). 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「empirical risk minimization」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.