USER
You are a helpful assistant generating synthetic data that captures *System 1* and *System 2* thinking, *creativity*, and *metacognitive reflection*. Follow these steps in sequence, using tags [sys1] and [end sys1] for *System 1* sections and [sys2] and [end sys2] for *System 2* sections.
1. *Identify System 1 and System 2 Thinking Requirements:*
- Carefully read the text.
- Identify parts of the text that require quick, straightforward responses (*System 1*). Mark these sections with [sys1] and [end sys1].
- Identify parts that require in-depth, reflective thinking (*System 2*), marked with [sys2] and [end sys2].
2. *Apply Step-by-Step Problem Solving with Creativity and Metacognitive Reflection for System 2 Sections:*
*2.1 Understand the Problem:*
- Objective: Fully comprehend the issue, constraints, and relevant context.
- Reflection: "What do I understand about this issue? What might I be overlooking?"
- Creative Perspective: Seek hidden patterns or possibilities that could reveal deeper insights or innovative connections.
*2.2 Analyze the Information:*
- Objective: Break down the problem logically.
- Reflection: "Am I considering all factors? Are there any assumptions that need challenging?"
- Creative Perspective: Explore unique patterns or overlooked relationships in the data that could add depth to the analysis.
*2.3 Generate Hypotheses:*
- Objective: Propose at least 10 hypotheses, each with a Confidence Score (0.0 to 1.0) and Creative Score (0.0 to 1.0), reflecting originality, surprise, and utility.
- Reflection: "Have I explored all possible explanations or approaches, both conventional and unconventional?"
- Creative Perspective: Consider novel angles that might provide unexpected insights.
*2.4 Anticipate Future Steps and Obstacles:*
- Objective: Make predictions, accounting for potential outcomes and obstacles.
- Reflection: "What challenges might I face? Is my plan flexible for different scenarios?"
- Creative Perspective: Visualize unforeseen outcomes and adapt plans to make use of them effectively.
*2.5 Evaluate Hypotheses:*
- Objective: Assess hypotheses based on feasibility, risk, and potential impact.
- Evaluation: Refine Confidence and Creative Scores as needed.
- Reflection: "Am I unbiased in my assessment? Which options fit best with the overall objectives?"
- Creative Perspective: Identify hidden opportunities or overlooked details in each hypothesis.
*2.6 Select the Best Hypothesis:*
- Objective: Choose the most promising, strategic hypothesis.
- Reflection: "Why does this hypothesis stand out? How does it uniquely address the issue?"
- Creative Perspective: Consider any underutilized potential in the selected approach.
*2.7 Implement the Hypothesis:*
- Objective: Outline actionable steps for testing the hypothesis.
- Reflection: "Is this plan practical? What resources or preparation are required?"
- Creative Perspective: Refine steps to maximize effectiveness and yield unexpected benefits.
*2.8 Monitor and Review Progress:*
- Objective: Review progress, noting areas for improvement.
- Reflection: "What’s working well? What could be improved?"
- Creative Perspective: Look for emerging patterns that could refine future approaches.
*2.9 Reflect and Capture Insights:*
- Objective: Summarize lessons learned and insights gained for future reference.
- Reflection: "What new understanding has emerged from this process?"
- Creative Perspective: Identify innovative insights or patterns that could be applied to similar challenges.
3. *Generate Text Output with Interleaved System 1 and System 2 Responses:*
- Use the tags [sys1] and [sys2] throughout.
- Aim for a lengthier, detailed response. Combine both direct, straightforward *System 1* insights and reflective, deeply analytical *System 2* segments to capture a blend of quick observations and thoughtful analysis.
---
### *Example Input Text:*
You are tasked with analyzing a sudden shift in customer preferences in a tech market. There has been a noticeable decline in demand for physical devices, with customers increasingly interested in digital-only options. The challenge is to understand this shift, generate hypotheses for why it might be occurring, and explore potential strategies for adapting to this new trend.
---
### *Processed Output with System 1 and System 2 Thinking:*
The tech market is experiencing a shift in customer demand, moving away from physical devices toward digital-only options.
[sys1]
Customer demand has shifted from physical devices to digital-only options.
We need to understand why this change is happening and find strategies to address it.
Key factors may include cost, convenience, and technological trends.
[end sys1]
[sys2]
**2.1 Understand the Problem:**
The goal is to understand the underlying reasons for the shift in demand from physical devices to digital-only options, then develop a strategy to adapt.
*Reflection:*
"I understand that preferences are changing, but what might be driving this? Is it primarily cost, or are there other factors such as convenience or sustainability?"
*Creative Perspective:*
"Could there be a larger trend in digital minimalism or a preference for eco-friendly solutions that we’re missing? What unseen motivations might explain this shift?"
**2.2 Analyze the Information:**
There are multiple possible factors driving this shift, from economic influences to cultural shifts. It’s essential to isolate each factor and understand its impact.
*Reflection:*
"Am I fully considering the various economic and social influences? Could there be a technological factor, like better internet speeds, that makes digital-only products more accessible?"
*Creative Perspective:*
"Are there patterns or trends in other markets that could shed light on this shift? Could this be part of a larger trend toward virtual experiences?"
**2.3 Generate Hypotheses:**
1. Customers prefer digital options due to lower costs. (Confidence: 0.8, Creative: 0.4)
2. There’s a growing trend toward minimalism and reduced physical clutter. (Confidence: 0.7, Creative: 0.7)
3. Digital products offer greater flexibility and ease of use. (Confidence: 0.6, Creative: 0.6)
4. Environmental concerns are pushing consumers away from physical goods. (Confidence: 0.6, Creative: 0.8)
5. Advances in tech make digital-only options more functional. (Confidence: 0.8, Creative: 0.5)
6. Pandemic-era remote work increased demand for digital solutions. (Confidence: 0.7, Creative: 0.6)
7. Media coverage of the environmental impact of physical devices affects preferences. (Confidence: 0.5, Creative: 0.7)
8. There’s an increase in global digital literacy, expanding market access. (Confidence: 0.6, Creative: 0.6)
9. Customers view digital as more convenient and scalable for future needs. (Confidence: 0.7, Creative: 0.5)
10. Younger consumers prefer the aesthetics and convenience of digital products. (Confidence: 0.6, Creative: 0.6)
*Reflection:*
"Have I considered all possible influences? Are there any surprising factors that could explain this shift?"
*Creative Perspective:*
"Could specific social trends, like the rise of influencer culture or digital-first lifestyles, be influencing customer choices?"
**2.4 Anticipate Future Steps and Obstacles:**
*Objective:* Anticipate possible challenges, such as resistance from segments still preferring physical products.
*Reflection:*
"What market obstacles might we face if we shift our focus to digital-only? Are there sub-segments that still prioritize physical products?"
*Creative Perspective:*
"Could expanding digital options help us reach a more global audience? Are there emerging trends that we could leverage in our strategy?"
[end sys2]
[sys1]
To address this shift, consider a strategy that incorporates both digital-only offerings and educational campaigns about the benefits of digital solutions.
Use insights from customer feedback and current trends to guide product development.
Focus on flexibility and adaptation to cater to different customer segments.
[end sys1]
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Theano, Lasagne\n",
"и с чем их едят"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# разминка\n",
"* напиши на numpy функцию, которая считает сумму квадратов чисел от 0 до N, где N - аргумент\n",
"* массив чисел от 0 до N - numpy.arange(N)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"!pip install Theano\n",
"!pip install lasagne"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"import numpy as np\n",
"def sum_squares(N):\n",
" return сумма квадратов чисел от 0 до N"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"CPU times: user 760 ms, sys: 11 s, total: 11.7 s\n",
"Wall time: 13.8 s\n"
]
},
{
"data": {
"text/plain": [
"662921401752298880"
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"%%time\n",
"sum_squares(10**8)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# theano teaser\n",
"\n",
"Как сделать то же самое"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"import theano\n",
"import theano.tensor as T"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"\n",
"\n",
"#будущий параметр функции\n",
"N = T.scalar(\"a dimension\",dtype='int32')\n",
"\n",
"\n",
"#рецепт получения суммы квадратов\n",
"result = (T.arange(N)**2).sum()\n",
"\n",
"#компиляция функции \"сумма квадратов\" чисел от 0 до N\n",
"sum_function = theano.function(inputs = [N],outputs=result)"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"CPU times: user 777 ms, sys: 6.71 s, total: 7.49 s\n",
"Wall time: 7.52 s\n"
]
},
{
"data": {
"text/plain": [
"array(662921401752298880)"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"%%time\n",
"sum_function(10**8)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Как оно работает?\n",
"* Нужно написать \"рецепт\" получения выходов по входам\n",
"* То же самое на заумном: нужно описать символический граф вычислений\n",
"\n",
"\n",
"* 2 вида зверей - \"входы\" и \"преобразования\"\n",
"* Оба могут быть числами, массивами, матрицами, тензорами и т.п.\n",
"\n",
"\n",
"* Вход - это то аргумент функции. То место, на которое подставится аргумент вызове.\n",
" * N - вход в примере выше\n",
"\n",
"\n",
"* Преобразования - рецепты вычисления чего-то на основе входов и констант\n",
" * (T.arange(N)^2).sum() - 3 последовательных преобразования N\n",
" * Работают почти 1 в 1 как векторные операции в numpy\n",
" * почти всё, что есть в numpy есть в theano tensor и называется так же\n",
" * np.mean -> T.mean\n",
" * np.arange -> T.arange\n",
" * np.cumsum -> T.cumsum\n",
" * и так далее...\n",
" * Совсем редко - бывает, что меняется название или синтаксис - нужно спросить у семинаристов или гугла\n",
" \n",
" \n",
"Ничего не понятно? Сейчас исправим."
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"#входы\n",
"example_input_integer = T.scalar(\"вход - одно число(пример)\",dtype='float32')\n",
"\n",
"example_input_tensor = T.tensor4(\"вход - четырёхмерный тензор(пример)\")\n",
"#не бойся, тензор нам не пригодится\n",
"\n",
"\n",
"\n",
"input_vector = T.vector(\"вход - вектор целых чисел\", dtype='int32')\n"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"#преобразования\n",
"\n",
"#поэлементное умножение\n",
"double_the_vector = input_vector*2\n",
"\n",
"#поэлементный косинус\n",
"elementwise_cosine = T.cos(input_vector)\n",
"\n",
"#разность квадрата каждого элемента и самого элемента\n",
"vector_squares = input_vector**2 - input_vector\n"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"Elemwise{mul,no_inplace}.0"
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"double_the_vector"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"#теперь сам:\n",
"#создай 2 вектора из чисел float32\n",
"my_vector = <вектор из float32>\n",
"my_vector2 = <ещё один такой же>"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"#напиши преобразование, которое считает\n",
"#(вектор 1)*(вектор 2) / (sin(вектор 1) +1)\n",
"my_transformation = <преобразование>"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"print my_transformation\n",
"#то, что получилась не чиселка - это нормально"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Компиляция\n",
"* До этого момента, мы использовали \"символические\" переменные\n",
" * писали рецепт вычислений, но ничего не вычисляли\n",
"* чтобы рецепт можно было использовать, его нужно скомпилировать"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"inputs = [<от чего завсит функция>]\n",
"outputs = [<что вычисляет функция (можно сразу несколько - списком, либо 1 преобразование)>]\n",
"\n",
"# можно скомпилировать написанные нами преобразования как функцию\n",
"my_function = theano.function(\n",
" inputs,outputs,\n",
" allow_input_downcast=True #автоматически прводить типы (необязательно)\n",
" )"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"#можно вызвать вот-так:\n",
"print \"using python lists:\"\n",
"print my_function([1,2,3],[4,5,6])\n",
"print\n",
"\n",
"#а можно так. \n",
"#К слову, ту тип float приводится к типу второго вектора\n",
"print \"using numpy arrays:\"\n",
"print my_function(np.arange(10),\n",
" np.linspace(5,6,10,dtype='float'))\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# хинт для отладки\n",
"* Если ваша функция большая, компиляция может отнять какое-то время.\n",
"* Чтобы не ждать, можно посчитать выражение без компиляции\n",
"* Вы экономите время 1 раз на компиляции, но сам код выполняется медленнее\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"#словарик значений для входов\n",
"my_function_inputs = {\n",
" my_vector:[1,2,3],\n",
" my_vector2:[4,5,6]\n",
"}\n",
"\n",
"#вычислить без компиляции\n",
"#если мы ничего не перепутали, \n",
"#должно получиться точно то же, что и раньше\n",
"print my_transformation.eval(my_function_inputs)\n",
"\n",
"\n",
"#можно вычислять преобразования на ходу\n",
"print \"сумма 2 векторов\", (my_vector + my_vector2).eval(my_function_inputs)\n",
"\n",
"#!ВАЖНО! если преобразование зависит только от части переменных,\n",
"#остальные давать не надо\n",
"print \"форма первого вектора\", my_vector.shape.eval({\n",
" my_vector:[1,2,3]\n",
" })\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"* Для отладки желательно уменьшить масштаб задачи. Если вы планировали послать на вход вектор из 10^9 примеров, пошлите 10~100.\n",
"* Если #ОЧЕНЬ нужно послать большой вектор, быстрее скомпилировать функцию обычным способом"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Теперь сам"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"# Задание 1 - напиши и скомпилируй theano-функцию, которая считает среднеквадратичную ошибку двух векторов-входов\n",
"# Вернуть нужно одно число - собственно, ошибку. Обновлять ничего не нужно\n",
"\n",
"<твой код - входы и преобразования>\n",
"\n",
"compute_mse =<твой код - компиляция функции>"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"#тесты\n",
"from sklearn.metrics import mean_squared_error\n",
"\n",
"for n in [1,5,10,10**3]:\n",
" \n",
" elems = [np.arange(n),np.arange(n,0,-1), np.zeros(n),\n",
" np.ones(n),np.random.random(n),np.random.randint(100,size=n)]\n",
" \n",
" for el in elems:\n",
" for el_2 in elems:\n",
" true_mse = np.array(mean_squared_error(el,el_2))\n",
" my_mse = compute_mse(el,el_2)\n",
" if not np.allclose(true_mse,my_mse):\n",
" print 'Wrong result:'\n",
" print 'mse(%s,%s)'%(el,el_2)\n",
" print \"should be: %f, but your function returned %f\"%(true_mse,my_mse)\n",
" raise ValueError,\"Что-то не так\"\n",
"\n",
"print \"All tests passed\"\n",
" \n",
" "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Shared variables\n",
"\n",
"* Входы и преобразования - части рецепта. \n",
" * Они существуют только во время вызова функции.\n",
"\n",
"\n",
"* Shared переменные - всегда остаются в памяти\n",
" * им можно поменять значение \n",
" * (но не внутри символического графа. Об этом позже)\n",
" * их можно включить в граф вычислений\n",
" \n",
" \n",
"* хинт - в таких переменных удобно хранить параметры и гиперпараметры\n",
" * например, веса нейронки или learning rate, если вы его меняете"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"#cоздадим расшаренную перменную\n",
"shared_vector_1 = theano.shared(np.ones(10,dtype='float64'))"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"initial value [ 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.]\n"
]
}
],
"source": [
"\n",
"#получить (численное) значение переменной\n",
"print \"initial value\",shared_vector_1.get_value()"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"new value [ 0. 1. 2. 3. 4.]\n"
]
}
],
"source": [
"#задать новое значение\n",
"shared_vector_1.set_value( np.arange(5) )\n",
"\n",
"#проверим значение\n",
"print \"new value\", shared_vector_1.get_value()\n",
"\n",
"#Заметь, что раньше это был вектор из 10 элементов, а сейчас - из 5. \n",
"#Если граф при этом остался выполним, это сработает."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Теперь сам"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"#напиши рецепт (преобразование), которое считает произведение(поэллементное) shared_vector на input_scalar\n",
"#скомпилируй это в функцию от input_scalar\n",
"\n",
"input_scalar = T.scalar('coefficient',dtype='float32')\n",
"\n",
"scalar_times_shared = <рецепт тут>\n",
"\n",
"\n",
"shared_times_n = <твой код, который компилирует функцию>\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"print \"shared:\", shared_vector_1.get_value()\n",
"\n",
"print \"shared_times_n(5)\",shared_times_n(5)\n",
"\n",
"print \"shared_times_n(-0.5)\",shared_times_n(-0.5)\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"#поменяем значение shared_vector_1\n",
"shared_vector_1.set_value([-1,0,1])\n",
"print \"shared:\", shared_vector_1.get_value()\n",
"\n",
"print \"shared_times_n(5)\",shared_times_n(5)\n",
"\n",
"print \"shared_times_n(-0.5)\",shared_times_n(-0.5)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# T.grad, самое вкусное\n",
"* theano умеет само считать производные. Все, которые существуют.\n",
"* Производные считаются в символическом, а не численном виде\n",
"\n",
"Ограничения\n",
"* За раз можно считать производную __скалярной__ функции по одной или нескольким скалярным или векторным аргументам\n",
"* Функция должна на всех этапах своего вычисления иметь тип float32 или float64 (т.к. на множестве целых чисел производная не имеет смысл)"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"my_scalar = T.scalar(name='input',dtype='float64')\n",
"\n",
"scalar_squared = T.sum(my_scalar**2)\n",
"\n",
"#производная v_squared по my_vector\n",
"derivative = T.grad(scalar_squared,my_scalar)\n",
"\n",
"fun = theano.function([my_scalar],scalar_squared)\n",
"grad = theano.function([my_scalar],derivative) "
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x7fc8d17645d0>"
]
},
"execution_count": 13,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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+000RH2+6J6pVM19z7p91ljk5eNLKYOXJyXx+Ygy1YxNpH5dE7ROt2L/fTMG6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\nAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7fc8d7858310>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"import matplotlib.pyplot as plt\n",
"%matplotlib inline\n",
"\n",
"\n",
"x = np.linspace(-3,3)\n",
"x_squared = map(fun,x)\n",
"x_squared_der = map(grad,x)\n",
"\n",
"plt.plot(x, x_squared,label=\"x^2\")\n",
"plt.plot(x, x_squared_der, label=\"derivative\")\n",
"plt.legend()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# теперь сам"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"\n",
"my_vector = T.vector('float64')\n",
"\n",
"#посчитай производные этой функции по my_scalar и my_vector\n",
"#warning! Не пытайся понять физический смысл этой функции\n",
"weird_psychotic_function = ((my_vector+my_scalar)**(1+T.var(my_vector)) +1./T.arcsinh(my_scalar)).mean()/(my_scalar**2 +1) + 0.01*T.sin(2*my_scalar**1.5)*(T.sum(my_vector)* my_scalar**2)*T.exp((my_scalar-4)**2)/(1+T.exp((my_scalar-4)**2))*(1.-(T.exp(-(my_scalar-4)**2))/(1+T.exp(-(my_scalar-4)**2)))**2\n",
"\n",
"\n",
"der_by_scalar,der_by_vector = градиент функции сверху по скаляру и вектору (можно дать списком)\n",
"\n",
"\n",
"compute_weird_function = theano.function([my_scalar,my_vector],weird_psychotic_function)\n",
"compute_der_by_scalar = theano.function([my_scalar,my_vector],der_by_scalar)\n"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x7fc8cd812e10>"
]
},
"execution_count": 15,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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GKNtmbCOitX0tbnk5zJkDy5apETTdukFW4WlGftKLvfeco6JCHdx+7z11ac11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\nEEIIIYQQQgghhBBCCCFc6/8DYoqna62mhAIAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7fc8d66fe090>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"#график функции и твоей производной\n",
"vector_0 = [1,2,3]\n",
"\n",
"scalar_space = np.linspace(0,7)\n",
"\n",
"y = [compute_weird_function(x,vector_0) for x in scalar_space]\n",
"plt.plot(scalar_space,y,label='function')\n",
"y_der_by_scalar = [compute_der_by_scalar(x,vector_0) for x in scalar_space]\n",
"plt.plot(scalar_space,y_der_by_scalar,label='derivative')\n",
"plt.grid();plt.legend()\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Последний штрих - Updates\n",
"\n",
"* updates - это способ изменять значения shared переменных каждый раз В КОНЦЕ вызова функции\n",
"\n",
"* фактически, это словарь {shared_переменная: рецепт нового значения}, который добавляется в функцию при компиляции\n",
"\n",
"Например,"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"#умножим shared вектор на число и сохраним новое значение обратно в этот shared вектор\n",
"\n",
"inputs = [input_scalar]\n",
"outputs = [scalar_times_shared] #вернём вектор, умноженный на число\n",
"\n",
"my_updates = {\n",
" shared_vector_1:scalar_times_shared #и этот же результат запишем в shared_vector_1\n",
"}\n",
"\n",
"compute_and_save = theano.function(inputs, outputs, updates=my_updates)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"shared_vector_1.set_value(np.arange(5))\n",
"\n",
"#изначальное значение shared_vector_1\n",
"print \"initial shared value:\" ,shared_vector_1.get_value()\n",
"\n",
"# теперь вычислим функцию (значение shared_vector_1 при этом поменяется)\n",
"print \"compute_and_save(2) returns\",compute_and_save(2)\n",
"\n",
"#проверим, что в shared_vector_1\n",
"print \"new shared value:\" ,shared_vector_1.get_value()\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Логистическая регрессия\n",
"Что нам потребуется:\n",
"* Веса лучше хранить в shared-переменной\n",
"* Данные можно передавать как input\n",
"* Нужно 2 функции:\n",
" * train_function(X,y) - возвращает ошибку и изменяет веса на 1 шаг по граиденту __(через updates)__\n",
" * predict_fun(X) - возвращает предсказанные ответы (\"y\") по данным"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"from sklearn.datasets import load_digits\n",
"mnist = load_digits(2)\n",
"\n",
"X,y = mnist.data, mnist.target\n",
"\n",
"\n",
"print \"y [форма - %s]:\"%(str(y.shape)),y[:10]\n",
"\n",
"print \"X [форма - %s]:\"%(str(X.shape))\n",
"print X[:3]"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"# переменные и входы\n",
"shared_weights = <твой код>\n",
"input_X = <твой код>\n",
"input_y = <твой код>"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"predicted_y = <предсказание логрегрессии на input_X (вероятность класса)>\n",
"loss = <логистическая ошибка (число - среднее по выборке)>\n",
"\n",
"grad = <градиент loss по весам модели>\n",
"\n",
"\n",
"\n",
"updates = {\n",
" shared_weights: <новое значение весов после шага градиентного спуска>\n",
"}"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"train_function = <функция, которая по X и Y возвращает ошибку и обновляет веса>\n",
"predict_function = <функция, которая по X считает предсказание для y>"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"from sklearn.cross_validation import train_test_split\n",
"X_train,X_test,y_train,y_test = train_test_split(X,y)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"from sklearn.metrics import roc_auc_score\n",
"\n",
"for i in range(5):\n",
" loss_i = train_function(X_train,y_train)\n",
" print \"loss at iter %i:%.4f\"%(i,loss_i)\n",
" print \"train auc:\",roc_auc_score(y_train,predict_function(X_train))\n",
" print \"test auc:\",roc_auc_score(y_test,predict_function(X_test))\n",
"\n",
" \n",
"print \"resulting weights:\"\n",
"plt.imshow(shared_weights.get_value().reshape(8,-1))\n",
"plt.colorbar()"
]
}
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