unit4 2 Udacity English Japanese

unit4 2YouTube↗ IA↗(long shot)
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Now we're going to talk about how to do inference on Bayes net.

ベイジアンネットワークの推論について説明しましょう

We'll start with our familiar network, and we'll talk about a method called enumeration.

まずはベイジアンネットワークと列挙法と呼ばれる

Which goes through all the possibilities, adds them up, and comes up with an answer.

すべての可能な場合を列挙して解を求める方法について解説します

So what we do is start by stating the problem. [BLANK_AUDIO]

では問題の定義から始めましょう

We're going to ask the question of, what is the probability that the burglar alarm occurred, given that John called and Mary called?

ここで取り上げる問題は “ジョンとメアリーがそれぞれ電話をしてきた時泥棒が侵入した確率はいくつか？”です

We'll use the definition of conditional probability to answer this.

この問題の解を得るためには条件付き確率を使います

So this query is equal to the joint probability distribution, [BLANK_AUDIO] Of all three variables divided by the conditionalized variables.

求める値は3つの変数の同時確率を条件となる変数の同時確率で割ったものになります

Now note, I'm using a notation here where, instead of writing out probability of some variable equals true,

ここではある変数の値が真である場合 “＝true”ではなく

I'm just using the notation+ and then the variable name in lowercase.

小文字で表した変数の頭文字eに＋を付加する記法を用います

And if I wanted the negation, I would use negation sign.

否定の場合は論理否定の記号“￢”を使います

Notice there's a different notation where, instead of writing out the + and negation signs, we just use the variable name itself, P(e) to indicate E is true.

この記法の代わりに変数名を使ってP（e）としその値が真だと表す記法もありますが

That notation works well but it can get confusing between does P(e) mean E is true, or does it mean E is a variable?

P（e）と書く場合 eが真であることを意味するのか単に変数を表すのかあいまいです

And so we're going to stick to the notation where we explicitly have the pluses and negation signs. To do inference by enumeration, we first take a conditional

そのためここでは＋と否定の記号￢を使った記法に従うことにします列挙法で推論を行うにはまず最初に問題を条件付き確率の式で表し

probability and rewrite it as unconditional probabilies.

それを条件付き確率を用いない形に書き換えます

Now, we enumerate all the atomic probabilities and calculate the sum of products.

すべての確率を列挙しそれぞれの積を求めその値の総和を算出します

Let's look at just the complex term on the numerator first.

まず複雑な分子の項をどのように計算するか見てみましょう

The procedure for figuring out the denominator would be similar and we'll skip that.

やり方は分子と同様なので分母は省略します

So the probability of these three terms together can be determined by enumerating all possible values of the hidden variables.

この3つの変数は潜在変数が取り得る値すべてを列挙することで求めることができます

In this case, there are two, e and a. So we'll sum over those variables for all values of e and for all values of a.

この場合EとAの2つですすべてのeの値とすべてのaの値を表す変数を足して合計を出しますが

In this case, they're Boolean, so there's only two values of each.

eとaはブーリアンなのでそれぞれ真と偽の2つの値に限られます

We ask what's the probability of this unconditional term?

続けてこの同時確率の値を求める式を追加し

And that we get by summing out over all possibilities, e and a being true or false. [BLANK_AUDIO]

eとaがそれぞれ真か偽で取り得る値すべてを足して総和を出します

Now to get the values of these atomic events,

この同時確率の値を求めるためには

we'll have to re-write this equation in a form that corresponds to the conditional probability tables that we have associated with the Bayes net.

ベイジアンネットワークの条件付き確率表に基づく式に書き換える必要があります

So we'll take this whole expression and re-write it.

ではこの式を書き換えていきましょう

It's still a sum over the hidden variables e and a, but now we'll rewrite

潜在変数eとaの総和はそのまま変わらず

this expression in terms of the parents of each of the nodes in the network.

それぞれのノードに従って同時確率を表す項を書き換えます

So that gives us the product of these five terms, which we then have to sum over all values of e and a.

これによって5つの項の積が得られ eとaの総和を求めることができます

If we call this product f(e,a), then the whole answer is the sum of f for all values, [BLANK_AUDIO]

仮にこの積をf（e，a）とすると求める答えは eとaが取り得るすべて値の総和fになります

Of e and a. So it's a sum of four terms where each of the terms is a product of five numbers.

従って答えは4つの項の和になりそれぞれの項は5つの値の積になっています

Where do we get the numbers to fill in this equation? >From the conditional probability table from our model.

この条件付き確率表を使えばそれぞれの数値を代入できるでしょう

So let's put the equation back up and we'll ask you for the case where both e and a are positive.

ではこの条件付き確率表を使って eとaが共に真である場合の

To look up in the conditional probability tables and fill in the numbers for each of these five terms. And then multiply them together and fill in the product.

5つの項のそれぞれの値とその積を求めてください