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xiangze/HMC_Theano.ipynb

Created June 19, 2014 13:26
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Hamilton Monte-Carlo by Theano
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HMC_Theano.ipynb
{
"metadata": {
"name": "HMC_Theano"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Theano Hamiltom Monte-Carlo"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Original code\n",
"http://deeplearning.net/tutorial/code/hmc/hmc.py"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\u82f1\u8a9e\u3067\u306e\u8aac\u660e(Original) http://deeplearning.net/tutorial/hmc.html"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import numpy\n",
"\n",
"from theano import function, shared\n",
"from theano import tensor as TT\n",
"import theano"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stderr",
"text": [
"Using gpu device 0: GeForce GT 620\n"
]
}
],
"prompt_number": 4
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"sharedX = lambda X, name: \\\n",
" shared(numpy.asarray(X, dtype=theano.config.floatX), name=name)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 5
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Hamiltonian"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\u904b\u52d5\u30a8\u30cd\u30eb\u30ae\u30fc\u3068\u30cf\u30df\u30eb\u30c8\u30cb\u30a2\u30f3\u306e\u5f0f\n",
"energy_fn\u306f\u30dd\u30c6\u30f3\u30b7\u30e3\u30eb\u30a8\u30cd\u30eb\u30ae\u30fc\u306e\u5f0f\u3067\u5916\u304b\u3089\u5165\u529b\u3059\u308b\u3002"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def kinetic_energy(vel):\n",
" \"\"\"Returns the kinetic energy associated with the given velocity\n",
" and mass of 1.\n",
"\n",
" Parameters\n",
" ----------\n",
" vel: theano matrix\n",
" Symbolic matrix whose rows are velocity vectors.\n",
"\n",
" Returns\n",
" -------\n",
" return: theano vector\n",
" Vector whose i-th entry is the kinetic entry associated with vel[i].\n",
"\n",
" \"\"\"\n",
" return 0.5 * (vel ** 2).sum(axis=1)\n",
"\n",
"\n",
"def hamiltonian(pos, vel, energy_fn):\n",
" \"\"\"\n",
" Returns the Hamiltonian (sum of potential and kinetic energy) for the given\n",
" velocity and position.\n",
"\n",
" Parameters\n",
" ----------\n",
" pos: theano matrix\n",
" Symbolic matrix whose rows are position vectors.\n",
" vel: theano matrix\n",
" Symbolic matrix whose rows are velocity vectors.\n",
" energy_fn: python function\n",
" Python function, operating on symbolic theano variables, used tox\n",
" compute the potential energy at a given position.\n",
"\n",
" Returns\n",
" -------\n",
" return: theano vector\n",
" Vector whose i-th entry is the Hamiltonian at position pos[i] and\n",
" velocity vel[i].\n",
" \"\"\"\n",
" # assuming mass is 1\n",
" return energy_fn(pos) + kinetic_energy(vel)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 6
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Metropolis-Hastings\u6cd5"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\u5909\u52d5\u304c\u53d7\u7406\u3055\u308c\u308b\u304b\u3069\u3046\u304b\u306e\u5224\u5b9a\u7d50\u679c\u3092\u8fd4\u3059(\u666e\u901a\u306eMCMC\u3068\u540c\u3058)\u3002"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def metropolis_hastings_accept(energy_prev, energy_next, s_rng):\n",
" \"\"\"\n",
" Performs a Metropolis-Hastings accept-reject move.\n",
"\n",
" Parameters\n",
" ----------\n",
" energy_prev: theano vector\n",
" Symbolic theano tensor which contains the energy associated with the\n",
" configuration at time-step t.\n",
" energy_next: theano vector\n",
" Symbolic theano tensor which contains the energy associated with the\n",
" proposed configuration at time-step t+1.\n",
" s_rng: theano.tensor.shared_randomstreams.RandomStreams\n",
" Theano shared random stream object used to generate the random number\n",
" used in proposal.\n",
"\n",
" Returns\n",
" -------\n",
" return: boolean\n",
" True if move is accepted, False otherwise\n",
" \"\"\"\n",
" ediff = energy_prev - energy_next\n",
" return (TT.exp(ediff) - s_rng.uniform(size=energy_prev.shape)) >= 0"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 7
},
{
"cell_type": "heading",
"level": 4,
"metadata": {},
"source": [
"simulate_dynamics\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"leapflog\u6cd5\u306b\u3088\u308b\u7a4d\u5206\u306e\u5b9f\u884c\u3000\u6700\u521d\u3068\u6700\u5f8c\u3060\u3051\u51e6\u7406\u3092\u5916\u5074\u306b\u66f8\u3044\u3066\u3044\u308b\u3002\n",
"\n",
"\u30dd\u30c6\u30f3\u30b7\u30e3\u30eb\u30a8\u30cd\u30eb\u30ae\u30fcenergy_fn\u306e\u5fae\u5206dE_dpos = TT.grad(energy_fn(pos).sum(), pos)\n",
"\n",
"theano.scan\u306f\u540c\u3058\u5f0f\u3092\u7e70\u308a\u8fd4\u3057\u5b9f\u884c\u3059\u308b\u305f\u3081\u306e\u95a2\u6570"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def simulate_dynamics(initial_pos, initial_vel, stepsize, n_steps, energy_fn):\n",
" \"\"\"\n",
" Return final (position, velocity) obtained after an `n_steps` leapfrog\n",
" updates, using Hamiltonian dynamics.\n",
"\n",
" Parameters\n",
" ----------\n",
" initial_pos: shared theano matrix\n",
" Initial position at which to start the simulation\n",
" initial_vel: shared theano matrix\n",
" Initial velocity of particles\n",
" stepsize: shared theano scalar\n",
" Scalar value controlling amount by which to move\n",
" energy_fn: python function\n",
" Python function, operating on symbolic theano variables, used to\n",
" compute the potential energy at a given position.\n",
"\n",
" Returns\n",
" -------\n",
" rval1: theano matrix\n",
" Final positions obtained after simulation\n",
" rval2: theano matrix\n",
" Final velocity obtained after simulation\n",
" \"\"\"\n",
"\n",
" def leapfrog(pos, vel, step):\n",
" \"\"\"\n",
" Inside loop of Scan. Performs one step of leapfrog update, using\n",
" Hamiltonian dynamics.\n",
"\n",
" Parameters\n",
" ----------\n",
" pos: theano matrix\n",
" in leapfrog update equations, represents pos(t), position at time t\n",
" vel: theano matrix\n",
" in leapfrog update equations, represents vel(t - stepsize/2),\n",
" velocity at time (t - stepsize/2)\n",
" step: theano scalar\n",
" scalar value controlling amount by which to move\n",
"\n",
" Returns\n",
" -------\n",
" rval1: [theano matrix, theano matrix]\n",
" Symbolic theano matrices for new position pos(t + stepsize), and\n",
" velocity vel(t + stepsize/2)\n",
" rval2: dictionary\n",
" Dictionary of updates for the Scan Op\n",
" \"\"\"\n",
" # from pos(t) and vel(t-stepsize/2), compute vel(t+stepsize/2)\n",
" dE_dpos = TT.grad(energy_fn(pos).sum(), pos)\n",
" new_vel = vel - step * dE_dpos\n",
" # from vel(t+stepsize/2) compute pos(t+stepsize)\n",
" new_pos = pos + step * new_vel\n",
" return [new_pos, new_vel], {}\n",
"\n",
" # compute velocity at time-step: t + stepsize/2\n",
" initial_energy = energy_fn(initial_pos)\n",
" dE_dpos = TT.grad(initial_energy.sum(), initial_pos)\n",
" vel_half_step = initial_vel - 0.5 * stepsize * dE_dpos\n",
"\n",
" # compute position at time-step: t + stepsize\n",
" pos_full_step = initial_pos + stepsize * vel_half_step\n",
"\n",
" # perform leapfrog updates: the scan op is used to repeatedly compute\n",
" # vel(t + (m-1/2)*stepsize) and pos(t + m*stepsize) for m in [2,n_steps].\n",
" (all_pos, all_vel), scan_updates = theano.scan(leapfrog,\n",
" outputs_info=[\n",
" dict(initial=pos_full_step),\n",
" dict(initial=vel_half_step),\n",
" ],\n",
" non_sequences=[stepsize],\n",
" n_steps=n_steps - 1)\n",
" final_pos = all_pos[-1]\n",
" final_vel = all_vel[-1]\n",
" # NOTE: Scan always returns an updates dictionary, in case the\n",
" # scanned function draws samples from a RandomStream. These\n",
" # updates must then be used when compiling the Theano function, to\n",
" # avoid drawing the same random numbers each time the function is\n",
" # called. In this case however, we consciously ignore\n",
" # \"scan_updates\" because we know it is empty.\n",
" assert not scan_updates\n",
"\n",
" # The last velocity returned by scan is vel(t +\n",
" # (n_steps - 1 / 2) * stepsize) We therefore perform one more half-step\n",
" # to return vel(t + n_steps * stepsize)\n",
" energy = energy_fn(final_pos)\n",
" final_vel = final_vel - 0.5 * stepsize * TT.grad(energy.sum(), final_pos)\n",
"\n",
" # return new proposal state\n",
" return final_pos, final_vel"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 8
},
{
"cell_type": "heading",
"level": 5,
"metadata": {},
"source": [
"hmc_move 1\u56de\u5206\u306e\u79fb\u52d5"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\u901f\u5ea6(\u904b\u52d5\u91cf)\u3092\u30e9\u30f3\u30c0\u30e0\u306b\u521d\u671f\u5316\u3057\u3001n_steps\u3060\u3051\u7a4d\u5206\u3092simulate_dynamics\u3067\u7e70\u308a\u8fd4\u3057\u3001accecpt\u3092\u5224\u5b9a\u3059\u308b\u3002"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def hmc_move(s_rng, positions, energy_fn, stepsize, n_steps):\n",
" \"\"\"\n",
" This function performs one-step of Hybrid Monte-Carlo sampling. We start by\n",
" sampling a random velocity from a univariate Gaussian distribution, perform\n",
" `n_steps` leap-frog updates using Hamiltonian dynamics and accept-reject\n",
" using Metropolis-Hastings.\n",
"\n",
" Parameters\n",
" ----------\n",
" s_rng: theano shared random stream\n",
" Symbolic random number generator used to draw random velocity and\n",
" perform accept-reject move.\n",
" positions: shared theano matrix\n",
" Symbolic matrix whose rows are position vectors.\n",
" energy_fn: python function\n",
" Python function, operating on symbolic theano variables, used to\n",
" compute the potential energy at a given position.\n",
" stepsize: shared theano scalar\n",
" Shared variable containing the stepsize to use for `n_steps` of HMC\n",
" simulation steps.\n",
" n_steps: integer\n",
" Number of HMC steps to perform before proposing a new position.\n",
"\n",
" Returns\n",
" -------\n",
" rval1: boolean\n",
" True if move is accepted, False otherwise\n",
" rval2: theano matrix\n",
" Matrix whose rows contain the proposed \"new position\"\n",
" \"\"\"\n",
"\n",
" # sample random velocity\n",
" initial_vel = s_rng.normal(size=positions.shape)\n",
"\n",
" # perform simulation of particles subject to Hamiltonian dynamics\n",
" final_pos, final_vel = simulate_dynamics(\n",
" initial_pos=positions,\n",
" initial_vel=initial_vel,\n",
" stepsize=stepsize,\n",
" n_steps=n_steps,\n",
" energy_fn=energy_fn)\n",
"\n",
" # accept/reject the proposed move based on the joint distribution\n",
" accept = metropolis_hastings_accept(\n",
" energy_prev=hamiltonian(positions, initial_vel, energy_fn),\n",
" energy_next=hamiltonian(final_pos, final_vel, energy_fn),\n",
" s_rng=s_rng)\n",
"\n",
" return accept, final_pos\n"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 9
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"step\u5e45\u3001accept\u306e\u6bd4\u7387(\u6e29\u5ea6\uff1f)\u3092\u9069\u5fdc\u7684\u306b\u5909\u3048\u3066\u3044\u308b\u3002"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def hmc_updates(positions, stepsize, avg_acceptance_rate, final_pos, accept,\n",
" target_acceptance_rate, stepsize_inc, stepsize_dec,\n",
" stepsize_min, stepsize_max, avg_acceptance_slowness):\n",
" \"\"\"This function is executed after `n_steps` of HMC sampling\n",
" (`hmc_move` function). It creates the updates dictionary used by\n",
" the `simulate` function. It takes care of updating: the position\n",
" (if the move is accepted), the stepsize (to track a given target\n",
" acceptance rate) and the average acceptance rate (computed as a\n",
" moving average).\n",
"\n",
" Parameters\n",
" ----------\n",
" positions: shared variable, theano matrix\n",
" Shared theano matrix whose rows contain the old position\n",
" stepsize: shared variable, theano scalar\n",
" Shared theano scalar containing current step size\n",
" avg_acceptance_rate: shared variable, theano scalar\n",
" Shared theano scalar containing the current average acceptance rate\n",
" final_pos: shared variable, theano matrix\n",
" Shared theano matrix whose rows contain the new position\n",
" accept: theano scalar\n",
" Boolean-type variable representing whether or not the proposed HMC move\n",
" should be accepted or not.\n",
" target_acceptance_rate: float\n",
" The stepsize is modified in order to track this target acceptance rate.\n",
" stepsize_inc: float\n",
" Amount by which to increment stepsize when acceptance rate is too high.\n",
" stepsize_dec: float\n",
" Amount by which to decrement stepsize when acceptance rate is too low.\n",
" stepsize_min: float\n",
" Lower-bound on `stepsize`.\n",
" stepsize_min: float\n",
" Upper-bound on `stepsize`.\n",
" avg_acceptance_slowness: float\n",
" Average acceptance rate is computed as an exponential moving average.\n",
" (1-avg_acceptance_slowness) is the weight given to the newest\n",
" observation.\n",
"\n",
" Returns\n",
" -------\n",
" rval1: dictionary-like\n",
" A dictionary of updates to be used by the `HMC_Sampler.simulate`\n",
" function. The updates target the position, stepsize and average\n",
" acceptance rate.\n",
"\n",
" \"\"\"\n",
"\n",
" ## POSITION UPDATES ##\n",
" # broadcast `accept` scalar to tensor with the same dimensions as\n",
" # final_pos.\n",
" accept_matrix = accept.dimshuffle(0, *(('x',) * (final_pos.ndim - 1)))\n",
" # if accept is True, update to `final_pos` else stay put\n",
" new_positions = TT.switch(accept_matrix, final_pos, positions)\n",
"\n",
" ## STEPSIZE UPDATES ##\n",
" # if acceptance rate is too low, our sampler is too \"noisy\" and we reduce\n",
" # the stepsize. If it is too high, our sampler is too conservative, we can\n",
" # get away with a larger stepsize (resulting in better mixing).\n",
" _new_stepsize = TT.switch(avg_acceptance_rate > target_acceptance_rate,\n",
" stepsize * stepsize_inc, stepsize * stepsize_dec)\n",
" # maintain stepsize in [stepsize_min, stepsize_max]\n",
" new_stepsize = TT.clip(_new_stepsize, stepsize_min, stepsize_max)\n",
"\n",
" ## ACCEPT RATE U+PDATES ##\n",
" # perform exponential moving average\n",
" mean_dtype = theano.scalar.upcast(accept.dtype, avg_acceptance_rate.dtype)\n",
" new_acceptance_rate = TT.add(\n",
" avg_acceptance_slowness * avg_acceptance_rate,\n",
" (1.0 - avg_acceptance_slowness) * accept.mean(dtype=mean_dtype))\n",
"\n",
" return [(positions, new_positions),\n",
" (stepsize, new_stepsize),\n",
" (avg_acceptance_rate, new_acceptance_rate)]"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 10
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"HMC_sampler"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"HMC\u306e\u30af\u30e9\u30b9\n",
"\n",
"hmc_move\u304c\u51fa\u529b\u3057\u305f\u5f0f\u3092 hmc_update\u3078\u5165\u529b\u3057\u3001\u5f0f\u3092\u7d44\u307f\u7acb\u3066\u3066\u3044\u308b\u3002\u305d\u306e\u51fa\u529b\u5f0f\u3092\u30b3\u30f3\u30d1\u30a4\u30eb\u3059\u308b\u3002 ( simulate = function([], [], updates=simulate_updates))\n",
"\n",
"s_rng = TT.shared_randomstreams.RandomStreams(seed)\n",
" \u306f\u4e71\u6570\u751f\u6210\u5668\n",
"\n",
"\u63cf\u753b(draw)\u306fsimulation\u5b9f\u884c\u3092\u542b\u3080\u3002"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"class HMC_sampler(object):\n",
" \"\"\"\n",
" Convenience wrapper for performing Hybrid Monte Carlo (HMC). It creates the\n",
" symbolic graph for performing an HMC simulation (using `hmc_move` and\n",
" `hmc_updates`). The graph is then compiled into the `simulate` function, a\n",
" theano function which runs the simulation and updates the required shared\n",
" variables.\n",
"\n",
" Users should interface with the sampler thorugh the `draw` function which\n",
" advances the markov chain and returns the current sample by calling\n",
" `simulate` and `get_position` in sequence.\n",
"\n",
" The hyper-parameters are the same as those used by Marc'Aurelio's\n",
" 'train_mcRBM.py' file (available on his personal home page).\n",
" \"\"\"\n",
"\n",
" def __init__(self, **kwargs):\n",
" self.__dict__.update(kwargs)\n",
"\n",
" @classmethod\n",
" def new_from_shared_positions(cls, shared_positions, energy_fn,\n",
" initial_stepsize=0.01, target_acceptance_rate=.9, n_steps=20,\n",
" stepsize_dec=0.98,\n",
" stepsize_min=0.001,\n",
" stepsize_max=0.25,\n",
" stepsize_inc=1.02,\n",
" # used in geometric avg. 1.0 would be not moving at all\n",
" avg_acceptance_slowness=0.9,\n",
" seed=12345):\n",
" \"\"\"\n",
" :param shared_positions: theano ndarray shared var with\n",
" many particle [initial] positions\n",
"\n",
" :param energy_fn:\n",
" callable such that energy_fn(positions)\n",
" returns theano vector of energies.\n",
" The len of this vector is the batchsize.\n",
"\n",
" The sum of this energy vector must be differentiable (with\n",
" theano.tensor.grad) with respect to the positions for HMC\n",
" sampling to work.\n",
"\n",
" \"\"\"\n",
" batchsize = shared_positions.shape[0]\n",
"\n",
" # allocate shared variables\n",
" stepsize = sharedX(initial_stepsize, 'hmc_stepsize')\n",
" avg_acceptance_rate = sharedX(target_acceptance_rate,\n",
" 'avg_acceptance_rate')\n",
" s_rng = TT.shared_randomstreams.RandomStreams(seed)\n",
"\n",
" # define graph for an `n_steps` HMC simulation\n",
" accept, final_pos = hmc_move(\n",
" s_rng,\n",
" shared_positions,\n",
" energy_fn,\n",
" stepsize,\n",
" n_steps)\n",
"\n",
" # define the dictionary of updates, to apply on every `simulate` call\n",
" simulate_updates = hmc_updates(\n",
" shared_positions,\n",
" stepsize,\n",
" avg_acceptance_rate,\n",
" final_pos=final_pos,\n",
" accept=accept,\n",
" stepsize_min=stepsize_min,\n",
" stepsize_max=stepsize_max,\n",
" stepsize_inc=stepsize_inc,\n",
" stepsize_dec=stepsize_dec,\n",
" target_acceptance_rate=target_acceptance_rate,\n",
" avg_acceptance_slowness=avg_acceptance_slowness)\n",
"\n",
" # compile theano function\n",
" simulate = function([], [], updates=simulate_updates)\n",
"\n",
" # create HMC_sampler object with the following attributes ...\n",
" return cls(\n",
" positions=shared_positions,\n",
" stepsize=stepsize,\n",
" stepsize_min=stepsize_min,\n",
" stepsize_max=stepsize_max,\n",
" avg_acceptance_rate=avg_acceptance_rate,\n",
" target_acceptance_rate=target_acceptance_rate,\n",
" s_rng=s_rng,\n",
" _updates=simulate_updates,\n",
" simulate=simulate)\n",
"\n",
" def draw(self, **kwargs):\n",
" \"\"\"\n",
" Returns a new position obtained after `n_steps` of HMC simulation.\n",
"\n",
" Parameters\n",
" ----------\n",
" kwargs: dictionary\n",
" The `kwargs` dictionary is passed to the shared variable\n",
" (self.positions) `get_value()` function. For example, to avoid\n",
" copying the shared variable value, consider passing `borrow=True`.\n",
"\n",
" Returns\n",
" -------\n",
" rval: numpy matrix\n",
" Numpy matrix whose of dimensions similar to `initial_position`.\n",
" \"\"\"\n",
" self.simulate()\n",
" return self.positions.get_value(borrow=False)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 11
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from IPython.display import display\n",
"\n",
"from sympy.interactive import printing\n",
"printing.init_printing(use_latex='mathjax')\n",
"from __future__ import division\n",
"import sympy as sym\n",
"from sympy import *\n",
"x, y, z, mu,C= symbols(\"x y z mu C\")"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 32
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Test"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"gaussian_energy(\u591a\u5909\u91cf\u6b63\u898f\u5206\u5e03)\u3092\u5f0f\u3068\u3057\u3066\u5165\u529b\u3001Test\u3059\u308b\u3002"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def sampler_on_nd_gaussian(sampler_cls, burnin, n_samples, dim=10):\n",
" batchsize=3\n",
"\n",
" rng = np.random.RandomState(123)\n",
"\n",
" # Define a covariance and mu for a gaussian\n",
" mu = np.array(rng.rand(dim) * 10, dtype=theano.config.floatX)\n",
" cov = np.array(rng.rand(dim, dim), dtype=theano.config.floatX)\n",
" cov = (cov + cov.T) / 2.\n",
" cov[numpy.arange(dim), numpy.arange(dim)] = 1.0\n",
" cov_inv = linalg.inv(cov)\n",
"\n",
" # Define energy function for a multi-variate Gaussian\n",
" def gaussian_energy(x):\n",
" return 0.5 * (TT.dot((x - mu), cov_inv) * (x - mu)).sum(axis=1)\n",
"\n",
" # Declared shared random variable for positions\n",
" position = shared(rng.randn(batchsize, dim).astype(theano.config.floatX))\n",
"\n",
" # Create HMC sampler\n",
" sampler = sampler_cls(position, gaussian_energy,\n",
" initial_stepsize=1e-3, stepsize_max=0.5)\n",
"\n",
" # Start with a burn-in process\n",
" garbage = [sampler.draw() for r in xrange(burnin)] #burn-in\n",
" # Draw `n_samples`: result is a 3D tensor of dim [n_samples, batchsize, dim]\n",
" _samples = np.asarray([sampler.draw() for r in xrange(n_samples)])\n",
" # Flatten to [n_samples * batchsize, dim]\n",
" samples = _samples.T.reshape(dim, -1).T\n",
"\n",
" print '****** TARGET VALUES ******'\n",
" print 'target mean:', mu\n",
" print 'target cov:\\n', cov\n",
"\n",
" print '****** EMPIRICAL MEAN/COV USING HMC ******'\n",
" print 'empirical mean: ', samples.mean(axis=0)\n",
" print 'empirical_cov:\\n', np.cov(samples.T)\n",
"\n",
" print '****** HMC INTERNALS ******'\n",
" print 'final stepsize', sampler.stepsize.get_value()\n",
" print 'final acceptance_rate', sampler.avg_acceptance_rate.get_value()\n",
"\n",
" return sampler\n",
"\n",
"def test_hmc():\n",
" sampler = sampler_on_nd_gaussian(HMC_sampler.new_from_shared_positions,\n",
" burnin=1000, n_samples=1000, dim=5)\n",
" assert abs(sampler.avg_acceptance_rate.get_value() -\n",
" sampler.target_acceptance_rate) < .1\n",
" assert sampler.stepsize.get_value() >= sampler.stepsize_min\n",
" assert sampler.stepsize.get_value() <= sampler.stepsize_max"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 13
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"\u7d50\u679c"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"target\u3068empirical\u306e\u5e73\u5747\u3001\u5206\u6563\u304c\u8fd1\u3044\u3053\u3068\u3092\u78ba\u8a8d\u3059\u308b\u3002"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"test_hmc()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stderr",
"text": [
"DEBUG: nvcc STDOUT tmpxft_00000d60_00000000-14_mod.ii\r\n",
"c:\\python27\\lib\\site-packages\\numpy\\core\\include\\numpy\\npy_1_7_deprecated_api.h(12) : Warning Msg: Using deprecated NumPy API, disable it by #defining NPY_NO_DEPRECATED_API NPY_1_7_API_VERSION\r\n",
" \u30e9\u30a4\u30d6\u30e9\u30ea C:/Users/xiangze/AppData/Local/Theano/compiledir_Windows-7-6.1.7601-SP1-Intel64_Family_6_Model_58_Stepping_9_GenuineIntel-2.7.3-32/tmpo60odh/7c27277b29e8aeb2a1a7da96533c8d73.lib \u3068\u30aa\u30d6\u30b8\u30a7\u30af\u30c8 C:/Users/xiangze/AppData/Local/Theano/compiledir_Windows-7-6.1.7601-SP1-Intel64_Family_6_Model_58_Stepping_9_GenuineIntel-2.7.3-32/tmpo60odh/7c27277b29e8aeb2a1a7da96533c8d73.exp \u3092\u4f5c\u6210\u4e2d\r\n",
"\n",
"DEBUG: nvcc STDOUT"
]
},
{
"output_type": "stream",
"stream": "stderr",
"text": [
" tmpxft_00000ef0_00000000-14_mod.ii\r\n",
"c:\\python27\\lib\\site-packages\\numpy\\core\\include\\numpy\\npy_1_7_deprecated_api.h(12) : Warning Msg: Using deprecated NumPy API, disable it by #defining NPY_NO_DEPRECATED_API NPY_1_7_API_VERSION\r\n",
" \u30e9\u30a4\u30d6\u30e9\u30ea C:/Users/xiangze/AppData/Local/Theano/compiledir_Windows-7-6.1.7601-SP1-Intel64_Family_6_Model_58_Stepping_9_GenuineIntel-2.7.3-32/tmpqt1vaa/3558c33881f15b7e821e74e77c19cc77.lib \u3068\u30aa\u30d6\u30b8\u30a7\u30af\u30c8 C:/Users/xiangze/AppData/Local/Theano/compiledir_Windows-7-6.1.7601-SP1-Intel64_Family_6_Model_58_Stepping_9_GenuineIntel-2.7.3-32/tmpqt1vaa/3558c33881f15b7e821e74e77c19cc77.exp \u3092\u4f5c\u6210\u4e2d\r\n",
"\n",
"DEBUG: nvcc STDOUT"
]
},
{
"output_type": "stream",
"stream": "stderr",
"text": [
" tmpxft_00001d20_00000000-14_mod.ii\r\n",
"c:\\python27\\lib\\site-packages\\numpy\\core\\include\\numpy\\npy_1_7_deprecated_api.h(12) : Warning Msg: Using deprecated NumPy API, disable it by #defining NPY_NO_DEPRECATED_API NPY_1_7_API_VERSION\r\n",
" \u30e9\u30a4\u30d6\u30e9\u30ea C:/Users/xiangze/AppData/Local/Theano/compiledir_Windows-7-6.1.7601-SP1-Intel64_Family_6_Model_58_Stepping_9_GenuineIntel-2.7.3-32/tmpkv0tdy/2b170d220db35c7ace9ed84acd87cc6b.lib \u3068\u30aa\u30d6\u30b8\u30a7\u30af\u30c8 C:/Users/xiangze/AppData/Local/Theano/compiledir_Windows-7-6.1.7601-SP1-Intel64_Family_6_Model_58_Stepping_9_GenuineIntel-2.7.3-32/tmpkv0tdy/2b170d220db35c7ace9ed84acd87cc6b.exp \u3092\u4f5c\u6210\u4e2d\r\n",
"\n",
"DEBUG: nvcc STDOUT"
]
},
{
"output_type": "stream",
"stream": "stderr",
"text": [
" tmpxft_00001424_00000000-14_mod.ii\r\n",
"c:\\python27\\lib\\site-packages\\numpy\\core\\include\\numpy\\npy_1_7_deprecated_api.h(12) : Warning Msg: Using deprecated NumPy API, disable it by #defining NPY_NO_DEPRECATED_API NPY_1_7_API_VERSION\r\n",
" \u30e9\u30a4\u30d6\u30e9\u30ea C:/Users/xiangze/AppData/Local/Theano/compiledir_Windows-7-6.1.7601-SP1-Intel64_Family_6_Model_58_Stepping_9_GenuineIntel-2.7.3-32/tmpc9zcur/34036322868fae939d1b54e75a65baea.lib \u3068\u30aa\u30d6\u30b8\u30a7\u30af\u30c8 C:/Users/xiangze/AppData/Local/Theano/compiledir_Windows-7-6.1.7601-SP1-Intel64_Family_6_Model_58_Stepping_9_GenuineIntel-2.7.3-32/tmpc9zcur/34036322868fae939d1b54e75a65baea.exp \u3092\u4f5c\u6210\u4e2d\r\n",
"\n",
"DEBUG: nvcc STDOUT"
]
},
{
"output_type": "stream",
"stream": "stderr",
"text": [
" tmpxft_00001c54_00000000-14_mod.ii\r\n",
"c:\\python27\\lib\\site-packages\\numpy\\core\\include\\numpy\\npy_1_7_deprecated_api.h(12) : Warning Msg: Using deprecated NumPy API, disable it by #defining NPY_NO_DEPRECATED_API NPY_1_7_API_VERSION\r\n",
" \u30e9\u30a4\u30d6\u30e9\u30ea C:/Users/xiangze/AppData/Local/Theano/compiledir_Windows-7-6.1.7601-SP1-Intel64_Family_6_Model_58_Stepping_9_GenuineIntel-2.7.3-32/tmpvy3qeh/3ea6a99a1a8d1d8523de8d72c27b90f4.lib \u3068\u30aa\u30d6\u30b8\u30a7\u30af\u30c8 C:/Users/xiangze/AppData/Local/Theano/compiledir_Windows-7-6.1.7601-SP1-Intel64_Family_6_Model_58_Stepping_9_GenuineIntel-2.7.3-32/tmpvy3qeh/3ea6a99a1a8d1d8523de8d72c27b90f4.exp \u3092\u4f5c\u6210\u4e2d\r\n",
"\n",
"DEBUG: nvcc STDOUT"
]
},
{
"output_type": "stream",
"stream": "stderr",
"text": [
" tmpxft_00001b58_00000000-14_mod.ii\r\n",
"c:\\python27\\lib\\site-packages\\numpy\\core\\include\\numpy\\npy_1_7_deprecated_api.h(12) : Warning Msg: Using deprecated NumPy API, disable it by #defining NPY_NO_DEPRECATED_API NPY_1_7_API_VERSION\r\n",
" \u30e9\u30a4\u30d6\u30e9\u30ea C:/Users/xiangze/AppData/Local/Theano/compiledir_Windows-7-6.1.7601-SP1-Intel64_Family_6_Model_58_Stepping_9_GenuineIntel-2.7.3-32/tmpek9dkq/d8c4ff295375d6d0172d15cb2f36cf45.lib \u3068\u30aa\u30d6\u30b8\u30a7\u30af\u30c8 C:/Users/xiangze/AppData/Local/Theano/compiledir_Windows-7-6.1.7601-SP1-Intel64_Family_6_Model_58_Stepping_9_GenuineIntel-2.7.3-32/tmpek9dkq/d8c4ff295375d6d0172d15cb2f36cf45.exp \u3092\u4f5c\u6210\u4e2d\r\n",
"\n",
"DEBUG: nvcc STDOUT"
]
},
{
"output_type": "stream",
"stream": "stderr",
"text": [
" tmpxft_00001668_00000000-14_mod.ii\r\n",
"c:\\python27\\lib\\site-packages\\numpy\\core\\include\\numpy\\npy_1_7_deprecated_api.h(12) : Warning Msg: Using deprecated NumPy API, disable it by #defining NPY_NO_DEPRECATED_API NPY_1_7_API_VERSION\r\n",
" \u30e9\u30a4\u30d6\u30e9\u30ea C:/Users/xiangze/AppData/Local/Theano/compiledir_Windows-7-6.1.7601-SP1-Intel64_Family_6_Model_58_Stepping_9_GenuineIntel-2.7.3-32/tmpbc2txg/21b45d3b456ca805c8174c0cd415d1d0.lib \u3068\u30aa\u30d6\u30b8\u30a7\u30af\u30c8 C:/Users/xiangze/AppData/Local/Theano/compiledir_Windows-7-6.1.7601-SP1-Intel64_Family_6_Model_58_Stepping_9_GenuineIntel-2.7.3-32/tmpbc2txg/21b45d3b456ca805c8174c0cd415d1d0.exp \u3092\u4f5c\u6210\u4e2d\r\n",
"\n",
"DEBUG: nvcc STDOUT"
]
},
{
"output_type": "stream",
"stream": "stderr",
"text": [
" tmpxft_00001a1c_00000000-14_mod.ii\r\n",
"c:\\python27\\lib\\site-packages\\numpy\\core\\include\\numpy\\npy_1_7_deprecated_api.h(12) : Warning Msg: Using deprecated NumPy API, disable it by #defining NPY_NO_DEPRECATED_API NPY_1_7_API_VERSION\r\n",
" \u30e9\u30a4\u30d6\u30e9\u30ea C:/Users/xiangze/AppData/Local/Theano/compiledir_Windows-7-6.1.7601-SP1-Intel64_Family_6_Model_58_Stepping_9_GenuineIntel-2.7.3-32/tmpwhqznw/6d3d177771405c8553790efdaefe218d.lib \u3068\u30aa\u30d6\u30b8\u30a7\u30af\u30c8 C:/Users/xiangze/AppData/Local/Theano/compiledir_Windows-7-6.1.7601-SP1-Intel64_Family_6_Model_58_Stepping_9_GenuineIntel-2.7.3-32/tmpwhqznw/6d3d177771405c8553790efdaefe218d.exp \u3092\u4f5c\u6210\u4e2d\r\n",
"\n",
"DEBUG: nvcc STDOUT"
]
},
{
"output_type": "stream",
"stream": "stderr",
"text": [
" tmpxft_00001204_00000000-14_mod.ii\r\n",
"c:\\python27\\lib\\site-packages\\numpy\\core\\include\\numpy\\npy_1_7_deprecated_api.h(12) : Warning Msg: Using deprecated NumPy API, disable it by #defining NPY_NO_DEPRECATED_API NPY_1_7_API_VERSION\r\n",
" \u30e9\u30a4\u30d6\u30e9\u30ea C:/Users/xiangze/AppData/Local/Theano/compiledir_Windows-7-6.1.7601-SP1-Intel64_Family_6_Model_58_Stepping_9_GenuineIntel-2.7.3-32/tmpxhhf5v/9545ace9247b8a41dce5d4a537389f08.lib \u3068\u30aa\u30d6\u30b8\u30a7\u30af\u30c8 C:/Users/xiangze/AppData/Local/Theano/compiledir_Windows-7-6.1.7601-SP1-Intel64_Family_6_Model_58_Stepping_9_GenuineIntel-2.7.3-32/tmpxhhf5v/9545ace9247b8a41dce5d4a537389f08.exp \u3092\u4f5c\u6210\u4e2d\r\n",
"\n",
"DEBUG: nvcc STDOUT"
]
},
{
"output_type": "stream",
"stream": "stderr",
"text": [
" tmpxft_00001458_00000000-14_mod.ii\r\n",
"c:\\python27\\lib\\site-packages\\numpy\\core\\include\\numpy\\npy_1_7_deprecated_api.h(12) : Warning Msg: Using deprecated NumPy API, disable it by #defining NPY_NO_DEPRECATED_API NPY_1_7_API_VERSION\r\n",
" \u30e9\u30a4\u30d6\u30e9\u30ea C:/Users/xiangze/AppData/Local/Theano/compiledir_Windows-7-6.1.7601-SP1-Intel64_Family_6_Model_58_Stepping_9_GenuineIntel-2.7.3-32/tmp022tza/6abc49f260f2dc095651555016e5b8a0.lib \u3068\u30aa\u30d6\u30b8\u30a7\u30af\u30c8 C:/Users/xiangze/AppData/Local/Theano/compiledir_Windows-7-6.1.7601-SP1-Intel64_Family_6_Model_58_Stepping_9_GenuineIntel-2.7.3-32/tmp022tza/6abc49f260f2dc095651555016e5b8a0.exp \u3092\u4f5c\u6210\u4e2d\r\n",
"\n",
"DEBUG: nvcc STDOUT"
]
},
{
"output_type": "stream",
"stream": "stderr",
"text": [
" tmpxft_00001460_00000000-14_mod.ii\r\n",
"c:\\python27\\lib\\site-packages\\numpy\\core\\include\\numpy\\npy_1_7_deprecated_api.h(12) : Warning Msg: Using deprecated NumPy API, disable it by #defining NPY_NO_DEPRECATED_API NPY_1_7_API_VERSION\r\n",
" \u30e9\u30a4\u30d6\u30e9\u30ea C:/Users/xiangze/AppData/Local/Theano/compiledir_Windows-7-6.1.7601-SP1-Intel64_Family_6_Model_58_Stepping_9_GenuineIntel-2.7.3-32/tmplydwbr/0ef32c1cf8d7c236d19dadf70411180e.lib \u3068\u30aa\u30d6\u30b8\u30a7\u30af\u30c8 C:/Users/xiangze/AppData/Local/Theano/compiledir_Windows-7-6.1.7601-SP1-Intel64_Family_6_Model_58_Stepping_9_GenuineIntel-2.7.3-32/tmplydwbr/0ef32c1cf8d7c236d19dadf70411180e.exp \u3092\u4f5c\u6210\u4e2d\r\n",
"\n",
"DEBUG: nvcc STDOUT"
]
},
{
"output_type": "stream",
"stream": "stderr",
"text": [
" tmpxft_00000f2c_00000000-14_mod.ii\r\n",
"c:\\python27\\lib\\site-packages\\numpy\\core\\include\\numpy\\npy_1_7_deprecated_api.h(12) : Warning Msg: Using deprecated NumPy API, disable it by #defining NPY_NO_DEPRECATED_API NPY_1_7_API_VERSION\r\n",
" \u30e9\u30a4\u30d6\u30e9\u30ea C:/Users/xiangze/AppData/Local/Theano/compiledir_Windows-7-6.1.7601-SP1-Intel64_Family_6_Model_58_Stepping_9_GenuineIntel-2.7.3-32/tmpn50lil/9b72d9e9a85baace3f2b14bd9b7781c6.lib \u3068\u30aa\u30d6\u30b8\u30a7\u30af\u30c8 C:/Users/xiangze/AppData/Local/Theano/compiledir_Windows-7-6.1.7601-SP1-Intel64_Family_6_Model_58_Stepping_9_GenuineIntel-2.7.3-32/tmpn50lil/9b72d9e9a85baace3f2b14bd9b7781c6.exp \u3092\u4f5c\u6210\u4e2d\r\n",
"\n",
"DEBUG: nvcc STDOUT"
]
},
{
"output_type": "stream",
"stream": "stderr",
"text": [
" tmpxft_000013ac_00000000-14_mod.ii\r\n",
"c:\\python27\\lib\\site-packages\\numpy\\core\\include\\numpy\\npy_1_7_deprecated_api.h(12) : Warning Msg: Using deprecated NumPy API, disable it by #defining NPY_NO_DEPRECATED_API NPY_1_7_API_VERSION\r\n",
" \u30e9\u30a4\u30d6\u30e9\u30ea C:/Users/xiangze/AppData/Local/Theano/compiledir_Windows-7-6.1.7601-SP1-Intel64_Family_6_Model_58_Stepping_9_GenuineIntel-2.7.3-32/tmpodkazg/406131ae89134f8d170001cd441504bc.lib \u3068\u30aa\u30d6\u30b8\u30a7\u30af\u30c8 C:/Users/xiangze/AppData/Local/Theano/compiledir_Windows-7-6.1.7601-SP1-Intel64_Family_6_Model_58_Stepping_9_GenuineIntel-2.7.3-32/tmpodkazg/406131ae89134f8d170001cd441504bc.exp \u3092\u4f5c\u6210\u4e2d\r\n",
"\n",
"DEBUG: nvcc STDOUT"
]
},
{
"output_type": "stream",
"stream": "stderr",
"text": [
" tmpxft_00001418_00000000-14_mod.ii\r\n",
"c:\\python27\\lib\\site-packages\\numpy\\core\\include\\numpy\\npy_1_7_deprecated_api.h(12) : Warning Msg: Using deprecated NumPy API, disable it by #defining NPY_NO_DEPRECATED_API NPY_1_7_API_VERSION\r\n",
" \u30e9\u30a4\u30d6\u30e9\u30ea C:/Users/xiangze/AppData/Local/Theano/compiledir_Windows-7-6.1.7601-SP1-Intel64_Family_6_Model_58_Stepping_9_GenuineIntel-2.7.3-32/tmprszspo/b31a6ab4861a29fd8ec22fef84c8b57c.lib \u3068\u30aa\u30d6\u30b8\u30a7\u30af\u30c8 C:/Users/xiangze/AppData/Local/Theano/compiledir_Windows-7-6.1.7601-SP1-Intel64_Family_6_Model_58_Stepping_9_GenuineIntel-2.7.3-32/tmprszspo/b31a6ab4861a29fd8ec22fef84c8b57c.exp \u3092\u4f5c\u6210\u4e2d\r\n",
"\n",
"C:\\Python27\\lib\\site-packages\\theano\\scan_module\\scan_perform_ext.py:85: RuntimeWarning: numpy.ndarray size changed, may indicate binary incompatibility\n",
" from scan_perform.scan_perform import *\n"
]
},
{
"output_type": "stream",
"stream": "stderr",
"text": [
"INFO (theano.gof.compilelock): Waiting for existing lock by unknown process (I am process '7336')\n"
]
},
{
"output_type": "stream",
"stream": "stderr",
"text": [
"INFO (theano.gof.compilelock): To manually release the lock, delete C:\\Users\\xiangze\\AppData\\Local\\Theano\\compiledir_Windows-7-6.1.7601-SP1-Intel64_Family_6_Model_58_Stepping_9_GenuineIntel-2.7.3-32\\lock_dir\n"
]
},
{
"output_type": "stream",
"stream": "stderr",
"text": [
"DEBUG: nvcc STDOUT tmpxft_00001a80_00000000-14_mod.ii\r\n",
"c:\\python27\\lib\\site-packages\\numpy\\core\\include\\numpy\\npy_1_7_deprecated_api.h(12) : Warning Msg: Using deprecated NumPy API, disable it by #defining NPY_NO_DEPRECATED_API NPY_1_7_API_VERSION\r\n",
" \u30e9\u30a4\u30d6\u30e9\u30ea C:/Users/xiangze/AppData/Local/Theano/compiledir_Windows-7-6.1.7601-SP1-Intel64_Family_6_Model_58_Stepping_9_GenuineIntel-2.7.3-32/tmpdvbcnw/b092474c94639a3000af125668a962c0.lib \u3068\u30aa\u30d6\u30b8\u30a7\u30af\u30c8 C:/Users/xiangze/AppData/Local/Theano/compiledir_Windows-7-6.1.7601-SP1-Intel64_Family_6_Model_58_Stepping_9_GenuineIntel-2.7.3-32/tmpdvbcnw/b092474c94639a3000af125668a962c0.exp \u3092\u4f5c\u6210\u4e2d\r\n",
"\n",
"DEBUG: nvcc STDOUT"
]
},
{
"output_type": "stream",
"stream": "stderr",
"text": [
" tmpxft_00000e1c_00000000-14_mod.ii\r\n",
"c:\\python27\\lib\\site-packages\\numpy\\core\\include\\numpy\\npy_1_7_deprecated_api.h(12) : Warning Msg: Using deprecated NumPy API, disable it by #defining NPY_NO_DEPRECATED_API NPY_1_7_API_VERSION\r\n",
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" \u30e9\u30a4\u30d6\u30e9\u30ea C:/Users/xiangze/AppData/Local/Theano/compiledir_Windows-7-6.1.7601-SP1-Intel64_Family_6_Model_58_Stepping_9_GenuineIntel-2.7.3-32/tmp4uglhl/5d21044a7b9bd64dda39fa9c69ed1908.lib \u3068\u30aa\u30d6\u30b8\u30a7\u30af\u30c8 C:/Users/xiangze/AppData/Local/Theano/compiledir_Windows-7-6.1.7601-SP1-Intel64_Family_6_Model_58_Stepping_9_GenuineIntel-2.7.3-32/tmp4uglhl/5d21044a7b9bd64dda39fa9c69ed1908.exp \u3092\u4f5c\u6210\u4e2d\r\n",
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" \u30e9\u30a4\u30d6\u30e9\u30ea C:/Users/xiangze/AppData/Local/Theano/compiledir_Windows-7-6.1.7601-SP1-Intel64_Family_6_Model_58_Stepping_9_GenuineIntel-2.7.3-32/tmpaaaw1m/968449afc2da0f3aca289a63edeb9828.lib \u3068\u30aa\u30d6\u30b8\u30a7\u30af\u30c8 C:/Users/xiangze/AppData/Local/Theano/compiledir_Windows-7-6.1.7601-SP1-Intel64_Family_6_Model_58_Stepping_9_GenuineIntel-2.7.3-32/tmpaaaw1m/968449afc2da0f3aca289a63edeb9828.exp \u3092\u4f5c\u6210\u4e2d\r\n",
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" \u30e9\u30a4\u30d6\u30e9\u30ea C:/Users/xiangze/AppData/Local/Theano/compiledir_Windows-7-6.1.7601-SP1-Intel64_Family_6_Model_58_Stepping_9_GenuineIntel-2.7.3-32/tmpqxravf/f871de19cf074c767d96444cfcda3814.lib \u3068\u30aa\u30d6\u30b8\u30a7\u30af\u30c8 C:/Users/xiangze/AppData/Local/Theano/compiledir_Windows-7-6.1.7601-SP1-Intel64_Family_6_Model_58_Stepping_9_GenuineIntel-2.7.3-32/tmpqxravf/f871de19cf074c767d96444cfcda3814.exp \u3092\u4f5c\u6210\u4e2d\r\n",
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" \u30e9\u30a4\u30d6\u30e9\u30ea C:/Users/xiangze/AppData/Local/Theano/compiledir_Windows-7-6.1.7601-SP1-Intel64_Family_6_Model_58_Stepping_9_GenuineIntel-2.7.3-32/tmpp3h6cy/68952e664e05c3179ad5a075bb3a038d.lib \u3068\u30aa\u30d6\u30b8\u30a7\u30af\u30c8 C:/Users/xiangze/AppData/Local/Theano/compiledir_Windows-7-6.1.7601-SP1-Intel64_Family_6_Model_58_Stepping_9_GenuineIntel-2.7.3-32/tmpp3h6cy/68952e664e05c3179ad5a075bb3a038d.exp \u3092\u4f5c\u6210\u4e2d\r\n",
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" \u30e9\u30a4\u30d6\u30e9\u30ea C:/Users/xiangze/AppData/Local/Theano/compiledir_Windows-7-6.1.7601-SP1-Intel64_Family_6_Model_58_Stepping_9_GenuineIntel-2.7.3-32/tmpfnfyuj/95729b1fa0d9f8886050c51ba23f1dc4.lib \u3068\u30aa\u30d6\u30b8\u30a7\u30af\u30c8 C:/Users/xiangze/AppData/Local/Theano/compiledir_Windows-7-6.1.7601-SP1-Intel64_Family_6_Model_58_Stepping_9_GenuineIntel-2.7.3-32/tmpfnfyuj/95729b1fa0d9f8886050c51ba23f1dc4.exp \u3092\u4f5c\u6210\u4e2d\r\n",
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" \u30e9\u30a4\u30d6\u30e9\u30ea C:/Users/xiangze/AppData/Local/Theano/compiledir_Windows-7-6.1.7601-SP1-Intel64_Family_6_Model_58_Stepping_9_GenuineIntel-2.7.3-32/tmpkdhoal/567ef094f4b8ef2dcaed704cc1aef872.lib \u3068\u30aa\u30d6\u30b8\u30a7\u30af\u30c8 C:/Users/xiangze/AppData/Local/Theano/compiledir_Windows-7-6.1.7601-SP1-Intel64_Family_6_Model_58_Stepping_9_GenuineIntel-2.7.3-32/tmpkdhoal/567ef094f4b8ef2dcaed704cc1aef872.exp \u3092\u4f5c\u6210\u4e2d\r\n",
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" \u30e9\u30a4\u30d6\u30e9\u30ea C:/Users/xiangze/AppData/Local/Theano/compiledir_Windows-7-6.1.7601-SP1-Intel64_Family_6_Model_58_Stepping_9_GenuineIntel-2.7.3-32/tmp7imwof/f003457c35f8c7750567cdb25827cc8c.lib \u3068\u30aa\u30d6\u30b8\u30a7\u30af\u30c8 C:/Users/xiangze/AppData/Local/Theano/compiledir_Windows-7-6.1.7601-SP1-Intel64_Family_6_Model_58_Stepping_9_GenuineIntel-2.7.3-32/tmp7imwof/f003457c35f8c7750567cdb25827cc8c.exp \u3092\u4f5c\u6210\u4e2d\r\n",
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"final stepsize 0.460446625948\n",
"final acceptance_rate 0.922501862049\n"
]
}
],
"prompt_number": 15
},
{
"cell_type": "code",
"collapsed": false,
"input": [],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 14
}
],
"metadata": {}
}
]
}
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