《Python神經(jīng)網(wǎng)絡(luò)》2——神經(jīng)元

雖然計(jì)算機(jī)擁有相對(duì)大量的電子計(jì)算元件、巨大的存儲(chǔ)空間，并且這些計(jì)算機(jī)的運(yùn)行頻率比肉蓬蓬、軟綿綿的生物大腦要快得多，但是即使是像鴿子一樣小的大腦，其能力也遠(yuǎn)遠(yuǎn)大于這些電子計(jì)算機(jī)。

專注于為中小企業(yè)提供網(wǎng)站設(shè)計(jì)制作、成都網(wǎng)站制作服務(wù),電腦端+手機(jī)端+微信端的三站合一,更高效的管理,為中小企業(yè)呼蘭免費(fèi)做網(wǎng)站提供優(yōu)質(zhì)的服務(wù)。我們立足成都，凝聚了一批互聯(lián)網(wǎng)行業(yè)人才，有力地推動(dòng)了上千家企業(yè)的穩(wěn)健成長(zhǎng)，幫助中小企業(yè)通過網(wǎng)站建設(shè)實(shí)現(xiàn)規(guī)模擴(kuò)充和轉(zhuǎn)變。

傳統(tǒng)的計(jì)算機(jī)按照嚴(yán)格的串行順序，相當(dāng)準(zhǔn)確具體地處理數(shù)據(jù)。對(duì)于這些冰冷堅(jiān)硬的計(jì)算機(jī)而言，不存在模糊性和不確定性。而另一方面，動(dòng)物的大腦表面上看起來以慢得多的節(jié)奏運(yùn)行，卻似乎以并行方式處理信號(hào)，模糊性是其計(jì)算的一種特征。

雖然神經(jīng)元有各種形式，但是所有的神經(jīng)元都是將電信號(hào)從一端傳輸?shù)搅硪欢?，沿著軸突，將電信號(hào)從樹突傳到樹突。然后，這些信號(hào)從?一個(gè)神經(jīng)元傳遞到另一個(gè)神經(jīng)元。

我們需要多少神經(jīng)元才能執(zhí)行相對(duì)復(fù)雜的有趣任務(wù)呢？

一般來說，能力非常強(qiáng)的人類大腦有大約1000億個(gè)神經(jīng)元！一只果蠅有約10萬個(gè)神經(jīng)元，能夠飛翔、覓食、躲避危險(xiǎn)、尋找食物以及執(zhí)行許多相當(dāng)復(fù)雜的任務(wù)。? 10萬個(gè)神經(jīng)元，這個(gè)數(shù)字恰好落在了現(xiàn)代計(jì)算機(jī)試圖復(fù)制的范圍內(nèi)。? ? 一只線蟲僅僅具有302個(gè)神經(jīng)元，與今天的數(shù)字計(jì)算資源相比，簡(jiǎn)直就是微乎其微！但是一直線蟲能夠完成一些相當(dāng)有用的任務(wù)，而這些任務(wù)對(duì)于尺寸大得多的傳統(tǒng)計(jì)算機(jī)程序而言卻難以完成。

激活函數(shù)：

階躍函數(shù)，S函數(shù)。

如何使用python做統(tǒng)計(jì)分析

Shape Parameters

形態(tài)參數(shù)

While a general continuous random variable can be shifted and scaled

with the loc and scale parameters, some distributions require additional

shape parameters. For instance, the gamma distribution, with density

γ(x,a)=λ(λx)a?1Γ(a)e?λx,

requires the shape parameter a. Observe that setting λ can be obtained by setting the scale keyword to 1/λ.

雖然一個(gè)一般的連續(xù)隨機(jī)變量可以被位移和伸縮通過loc和scale參數(shù)，但一些分布還需要額外的形態(tài)參數(shù)。作為例子，看到這個(gè)伽馬分布，這是它的密度函數(shù)

γ(x,a)=λ(λx)a?1Γ(a)e?λx,

要求一個(gè)形態(tài)參數(shù)a。注意到λ的設(shè)置可以通過設(shè)置scale關(guān)鍵字為1/λ進(jìn)行。

Let’s check the number and name of the shape parameters of the gamma

distribution. (We know from the above that this should be 1.)

讓我們檢查伽馬分布的形態(tài)參數(shù)的名字的數(shù)量。（我們知道從上面知道其應(yīng)該為1）

from scipy.stats import gamma

gamma.numargs

1

gamma.shapes

'a'

Now we set the value of the shape variable to 1 to obtain the

exponential distribution, so that we compare easily whether we get the

results we expect.

現(xiàn)在我們?cè)O(shè)置形態(tài)變量的值為1以變成指數(shù)分布。所以我們可以容易的比較是否得到了我們所期望的結(jié)果。

gamma(1, scale=2.).stats(moments="mv")

(array(2.0), array(4.0))

Notice that we can also specify shape parameters as keywords:

注意我們也可以以關(guān)鍵字的方式指定形態(tài)參數(shù)：

gamma(a=1, scale=2.).stats(moments="mv")

(array(2.0), array(4.0))

Freezing a Distribution

凍結(jié)分布

Passing the loc and scale keywords time and again can become quite

bothersome. The concept of freezing a RV is used to solve such problems.

不斷地傳遞loc與scale關(guān)鍵字最終會(huì)讓人厭煩。而凍結(jié)RV的概念被用來解決這個(gè)問題。

rv = gamma(1, scale=2.)

By using rv we no longer have to include the scale or the shape

parameters anymore. Thus, distributions can be used in one of two ways,

either by passing all distribution parameters to each method call (such

as we did earlier) or by freezing the parameters for the instance of the

distribution. Let us check this:

通過使用rv我們不用再更多的包含scale與形態(tài)參數(shù)在任何情況下。顯然，分布可以被多種方式使用，我們可以通過傳遞所有分布參數(shù)給對(duì)方法的每次調(diào)用（像我們之前做的那樣）或者可以對(duì)一個(gè)分布對(duì)象凍結(jié)參數(shù)。讓我們看看是怎么回事：

rv.mean(), rv.std()

(2.0, 2.0)

This is indeed what we should get.

這正是我們應(yīng)該得到的。

Broadcasting

廣播

The basic methods pdf and so on satisfy the usual numpy broadcasting

rules. For example, we can calculate the critical values for the upper

tail of the t distribution for different probabilites and degrees of

freedom.

像pdf這樣的簡(jiǎn)單方法滿足numpy的廣播規(guī)則。作為例子，我們可以計(jì)算t分布的右尾分布的臨界值對(duì)于不同的概率值以及自由度。

stats.t.isf([0.1, 0.05, 0.01], [[10], [11]])

array([[ 1.37218364, 1.81246112, 2.76376946],

[ 1.36343032, 1.79588482, 2.71807918]])

Here, the first row are the critical values for 10 degrees of freedom

and the second row for 11 degrees of freedom (d.o.f.). Thus, the

broadcasting rules give the same result of calling isf twice:

這里，第一行是以10自由度的臨界值，而第二行是以11為自由度的臨界值。所以，廣播規(guī)則與下面調(diào)用了兩次isf產(chǎn)生的結(jié)果相同。

stats.t.isf([0.1, 0.05, 0.01], 10)

array([ 1.37218364, 1.81246112, 2.76376946])

stats.t.isf([0.1, 0.05, 0.01], 11)

array([ 1.36343032, 1.79588482, 2.71807918])

If the array with probabilities, i.e, [0.1, 0.05, 0.01] and the array of

degrees of freedom i.e., [10, 11, 12], have the same array shape, then

element wise matching is used. As an example, we can obtain the 10% tail

for 10 d.o.f., the 5% tail for 11 d.o.f. and the 1% tail for 12 d.o.f.

by calling

但是如果概率數(shù)組，如[0.1,0.05,0.01]與自由度數(shù)組,如[10,11,12]具有相同的數(shù)組形態(tài)，則元素對(duì)應(yīng)捕捉被作用，我們可以分別得到10%，5%，1%尾的臨界值對(duì)于10，11,12的自由度。

stats.t.isf([0.1, 0.05, 0.01], [10, 11, 12])

array([ 1.37218364, 1.79588482, 2.68099799])

Specific Points for Discrete Distributions

離散分布的特殊之處

Discrete distribution have mostly the same basic methods as the

continuous distributions. However pdf is replaced the probability mass

function pmf, no estimation methods, such as fit, are available, and

scale is not a valid keyword parameter. The location parameter, keyword

loc can still be used to shift the distribution.

離散分布的簡(jiǎn)單方法大多數(shù)與連續(xù)分布很類似。當(dāng)然像pdf被更換為密度函數(shù)pmf，沒有估計(jì)方法，像fit是可用的。而scale不是一個(gè)合法的關(guān)鍵字參數(shù)。Location參數(shù)，關(guān)鍵字loc則仍然可以使用用于位移。

The computation of the cdf requires some extra attention. In the case of

continuous distribution the cumulative distribution function is in most

standard cases strictly monotonic increasing in the bounds (a,b) and

has therefore a unique inverse. The cdf of a discrete distribution,

however, is a step function, hence the inverse cdf, i.e., the percent

point function, requires a different definition:

ppf(q) = min{x : cdf(x) = q, x integer}

Cdf的計(jì)算要求一些額外的關(guān)注。在連續(xù)分布的情況下，累積分布函數(shù)在大多數(shù)標(biāo)準(zhǔn)情況下是嚴(yán)格遞增的，所以有唯一的逆。而cdf在離散分布，無論如何，是階躍函數(shù)，所以cdf的逆，分位點(diǎn)函數(shù)，要求一個(gè)不同的定義：

ppf(q) = min{x : cdf(x) = q, x integer}

For further info, see the docs here.

為了更多信息可以看這里。

We can look at the hypergeometric distribution as an example

from scipy.stats import hypergeom

[M, n, N] = [20, 7, 12]

我們可以看這個(gè)超幾何分布的例子

from scipy.stats import hypergeom

[M, n, N] = [20, 7, 12]

If we use the cdf at some integer points and then evaluate the ppf at

those cdf values, we get the initial integers back, for example

如果我們使用在一些整數(shù)點(diǎn)使用cdf，它們的cdf值再作用ppf會(huì)回到開始的值。

x = np.arange(4)*2

x

array([0, 2, 4, 6])

prb = hypergeom.cdf(x, M, n, N)

prb

array([ 0.0001031991744066, 0.0521155830753351, 0.6083591331269301,

0.9897832817337386])

hypergeom.ppf(prb, M, n, N)

array([ 0., 2., 4., 6.])

If we use values that are not at the kinks of the cdf step function, we get the next higher integer back:

如果我們使用的值不是cdf的函數(shù)值，則我們得到一個(gè)更高的值。

hypergeom.ppf(prb + 1e-8, M, n, N)

array([ 1., 3., 5., 7.])

hypergeom.ppf(prb - 1e-8, M, n, N)

array([ 0., 2., 4., 6.])

python單位階躍函數(shù)

round()函數(shù)用錯(cuò)了啊，你應(yīng)該寫成：

lb = round(fx*2.205, 2)

這樣。

round(x[, n])

Return the floating point value x rounded to n digits after the decimal point. If n is omitted, it defaults to zero. Delegates to x.__round__(n).

For the built-in types supporting round(), values are rounded to the closest multiple of 10 to the power minus n; if two multiples are equally close, rounding is done toward the even choice (so, for example, both round(0.5) and round(-0.5) are 0, and round(1.5) is 2). The return value is an integer if called with one argument, otherwise of the same type as x.

如果對(duì)您有幫助，請(qǐng)記得采納為滿意答案，謝謝！祝您生活愉快！

python 的階躍函數(shù)怎么寫

def?f(T):

def?wrap(t):

if?t??0?and?t??T?/?2:?return?1

elif?t?==?T?/?2:?return?0

else:return?-1

return?wrap

if?__name__?==?'__main__':

d?=?f(2)

print?d(2)