Unit 4, 1 Probabilistic Inference knowitvideos English Japanese

Unit 4, 1 Probabilistic InferenceYouTube↗ IA↗(long shot)
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[Probabilistic Interference]

再びようこそ

[Male] Welcome back. In the previous unit, we went over the basics of probability theory and saw how a Bayes network could concisely represent a joint probability distribution, including the representation of independence between the variables.

前回のレッスンでは確率論の基本的な要点について学びましたまたベイジアンネットワークを使って同時確率分布や変数の独立関係を簡潔に表現する方法を考察しました

In this unit, we will see how to do probabilistic inference.

今回のレッスンではどのように確率的推論を行うか

That is, how to answer probability questions using Bayes nets.

ベイジアンネットワークを使って確率の問題を解く方法を学びます

Let's put up a simple Bayes net.

まず簡単な例を挙げましょう

We'll use the familiar example of the earthquake

身近なところで地震を例にします

where we can have a burglary or an earthquake

泥棒と地震に反応して鳴るアラームを設定し

setting off an alarm, and if the alarm goes off,

アラームが鳴り響くと

either John or Mary might call.

ジョンかメアリーが電話をかけます

Now, what kinds of questions can we ask to do inference about?

この場合どんな問題を元に推論ができるでしょう？

The simplest type of question is the same question we ask

最も単純なタイプの問題は

with an ordinary subroutine or function in a programming language.

プログラミング言語のサブルーチンや関数を用いたものです

Namely, given some inputs, what are the outputs?

つまりある入力に対し何が出力されるかという問題です

So, in this case, we could say given the inputs of B and E,

従ってここではBとEの入力に対し

what are the outputs, J and M?

出力のJとMはどうなるかが問題になります

Rather than call them input and output variables,

確率的推論では入力や出力を

in probabilistic inference, we'll call them evidence and query variables.

それぞれ説明変数と目的変数と呼びます

That is, the variables that we know the values of are the evidence,

値が分かっている変数を説明変数

and the ones that we want to find out the values of are the query variables.

これから求める変数を目的変数と呼ぶわけです

Anything that is neither evidence nor query is known as a hidden variable.

説明変数でも目的変数でもないものは潜在変数と言います

That is, we won't tell you what its value is.

潜在変数の値は知らされませんし

We won't figure out what its value is and report it,

その数値を算出する必要もありませんが

but we'll have to compute with it internally.

計算の過程では算出しなければなりません

And now furthermore, in probabilistic inference,

そして確率的推論においては

the output is not a single number for each of the query variables,

出力はそれぞれの目的変数に対する単一の値ではなく

but rather, it's a probability distribution.

その変数の確率分布となります

So, the answer is going to be a complete, joint probability distribution

従って答えは目的変数全体にわたる

over the query variables.

完全なる同時確率分布です

We call this the posterior distribution, given the evidence,

これを説明変数が与えられた時の事後分布と呼び

and we can write it like this.

このように書き表します

It's the probability distribution of one or more query variables

確率を表すPを頭に 1つまたは複数の目的変数Qを並べ

given the values of the evidence variables.

与えられた説明変数とその値を連ねます

And there can be zero or more evidence variables,

説明変数は0個以上で

and each of them are given an exact value.

それぞれの数値が与えられます

And that's the computation we want to come up with.

これが答えを求める計算式となります

There's another question we can ask.

考えられる問題は他にもあります

Which is the most likely explanation?

もっともらしい説明はどれか

That is, out of all the possible values for all the query variables,

つまり可能な目的変数の組み合わせのうち

which combination of values has the highest probability?

どの組が最も高い確率になるかという問題です

We write the formula like this, asking which Q values

この式を使ってどの説明変数が

are maxable given the evidence values.

目的変数を最大化するか求めます

Now, in an ordinary programming language, each function goes only one way.

通常のプログラミング言語では関数は1つの方向にしか進みません

It has input variables, does some computation,

関数は入力変数を受け取って何らかの計算を行い

and comes up with a result variable or result variables.

出力変数を算出します

One great thing about Bayes nets is that we're not restricted

ベイジアンネットワークの長所はこの1方向性に

to going only in one direction.

制限されないことです

We could go in the causal direction, giving as evidence the route nodes of the tree and asking as query values the nodes at the bottom.

因果関係に従って木の最上位にあるノードを説明変数最下位のノードを目的変数にできますし

Or, we could reverse that causal flow.

結果から原因の逆方向に戻ることも可能です

For example, we could have J and M be the evidence variables

仮にJとMを説明変数にした場合

and B and E be the query variables,

BとEを目的変数にすることもできますし

or we could have any other combination.

他の組み合わせも可能になります

For example, we could have M be the evidence variable

例えばMを説明変数にして

and J and B be the query variables.

JとBを目的変数にすることも可能なのです

Here's a question for you.

ではここで問題です

Imagine the situation where Mary has called to report that the alarm is going off,

アラームが鳴りメアリーが電話をかけてきたとしましょう

and we want to know whether or not there has been a burglary.

ここで知りたいのは泥棒が入ったかどうかです

For each of the nodes, click on the circle to tell us

それぞれのノードについて

if the node is an evidence node, a hidden node,

説明変数か潜在変数か

or a query node.

それとも目的変数か分類してください

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