diff --git a/.idea/misc.xml b/.idea/misc.xml index 8a7d0cb..cf86b06 100644 --- a/.idea/misc.xml +++ b/.idea/misc.xml @@ -1,7 +1,7 @@ - + - + \ No newline at end of file diff --git a/.idea/sportran.iml b/.idea/sportran.iml index 9502469..9b74217 100644 --- a/.idea/sportran.iml +++ b/.idea/sportran.iml @@ -2,7 +2,7 @@ - + @@ -12,4 +12,4 @@ - + \ No newline at end of file diff --git a/examples/08_example_optimize_prior .ipynb b/examples/08_example_optimize_prior .ipynb index 0e9304f..51625be 100644 --- a/examples/08_example_optimize_prior .ipynb +++ b/examples/08_example_optimize_prior .ipynb @@ -153,7 +153,7 @@ " Iterations: 129\n", " Function evaluations: 4464\n", " Gradient evaluations: 144\n", - "AIC: -75099.3659903142; Steps since last AIC update: 0\n", + "AIC: -75099.3829298082; Steps since last AIC update: 0\n", "n_parameters = 6\n", "Spline nodes are equispaced from 0 to the Nyquist frequency.\n", "Optimization terminated successfully.\n", @@ -161,14 +161,14 @@ " Iterations: 158\n", " Function evaluations: 6290\n", " Gradient evaluations: 170\n", - "AIC: -74942.16206470405; Steps since last AIC update: 0\n", + "AIC: -74942.18914571461; Steps since last AIC update: 0\n", "-----------------------------------------------------\n", " MAXIMUM LIKELIHOOD ESTIMATION\n", "-----------------------------------------------------\n", " Fixed n_parameters = 6\n", - " S_{00} = 972767.289072 +/- 44343.082278\n", - " S_{01} = 167917.403774 +/- 25834.235931\n", - " S_{11} = 642387.799921 +/- 27425.049491\n", + " S_{00} = 966435.259470 +/- 43024.546465\n", + " S_{01} = 165167.050461 +/- 25564.667000\n", + " S_{11} = 641284.553121 +/- 27304.628630\n", "-----------------------------------------------------\n", "\n" ] @@ -195,133 +195,22 @@ }, { "cell_type": "code", - "execution_count": 61, - "metadata": {}, - "outputs": [], - "source": [ - "def reweight_alpha_vec(alpha, samples):\n", - " truth_mean = np.mean(samples.T[:,:]*np.exp(-alpha[:, None, None]*np.linalg.norm(samples, axis=1)**2), axis=2)\\\n", - " /np.mean(np.exp(-alpha[:, None, None]*np.linalg.norm(samples, axis=1)**2), axis=2)\n", - " truth_var = np.mean(samples.T[:,:]**2*np.exp(-alpha[:, None, None]*np.linalg.norm(samples, axis=1)**2), axis=2)\\\n", - " /np.mean(np.exp(-alpha[:, None, None]*np.linalg.norm(samples, axis=1)**2), axis=2)-truth_mean**2\n", - " return truth_mean, truth_var\n", - "\n", - "def reweight_logev_alpha_vec(alpha, samples):\n", - " M = samples.shape[1]\n", - " truth_mean = np.log(np.mean(np.exp(-alpha[:, None]*np.linalg.norm(samples, axis=1)**2), axis=1)) + M/2 * np.log(alpha/2/np.pi)\n", - " return truth_mean\n", - "\n", - "def reweight_alpha(alpha, samples):\n", - " truth_mean = np.mean(samples.T[:,:]*np.exp(-alpha*np.linalg.norm(samples, axis=1)**2), axis=1)\\\n", - " /np.mean(np.exp(-alpha*np.linalg.norm(samples, axis=1)**2), axis=0)\n", - " truth_var = np.mean(samples.T[:,:]**2*np.exp(-alpha*np.linalg.norm(samples, axis=1)**2), axis=1)\\\n", - " /np.mean(np.exp(-alpha*np.linalg.norm(samples, axis=1)**2), axis=0)-truth_mean**2\n", - " return truth_mean, truth_var" - ] - }, - { - "cell_type": "code", - "execution_count": 62, - "metadata": {}, - "outputs": [], - "source": [ - "def generate_samples_mc(model, w, omega, omega_fixed, n, cov_w, size=1000):\n", - " sample = w + np.random.multivariate_normal(mean=np.zeros_like(w), cov=cov_w, size=size)\n", - " #sample_S = np.stack([scale_matrix(model, ww, omega, omega_fixed, 2)[:, 1, 0]/scale_matrix(model, ww, omega, omega_fixed, 2)[:, 1, 1] for ww in sample])\n", - " \n", - " return sample" - ] - }, - { - "cell_type": "code", - "execution_count": 63, - "metadata": {}, - "outputs": [], - "source": [ - "from sportran.md.maxlike import scale_matrix" - ] - }, - { - "cell_type": "code", - "execution_count": 64, - "metadata": {}, - "outputs": [], - "source": [ - "sampples=generate_samples_mc(flux_resample.maxlike.model,\n", - " flux_resample.maxlike.parameters_mean,\n", - " flux_resample.maxlike.omega,\n", - " flux_resample.maxlike.omega_fixed,\n", - " flux_resample.N_CURRENTS,\n", - " flux_resample.maxlike.parameters_cov\n", - " ) " - ] - }, - { - "cell_type": "code", - "execution_count": 65, + "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "(1000, 18)" + "" ] }, - "execution_count": 65, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "sampples.shape" - ] - }, - { - "cell_type": "code", - "execution_count": 71, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[1.00000000e-10 1.10009001e-09 2.10018002e-09 ... 9.99799982e-06\n", - " 9.99899991e-06 1.00000000e-05]\n", - "[9.99121488e-01 9.90377933e-01 9.81710912e-01 ... 1.73263622e-38\n", - " 1.71779560e-38 1.70308213e-38]\n", - "1.0261923492349234e-06\n" - ] - } - ], - "source": [ - "dic_alpha={}\n", - "\n", - "alpha = np.linspace(1e-10,1e-5,10000)\n", - "dic_alpha['lev_s']=reweight_logev_alpha_vec(alpha=alpha,\n", - " samples=sampples\n", - " )\n", - "dic_alpha['alpha_s'] = alpha[np.argmax(dic_alpha['lev_s'])]\n", - "print(dic_alpha['alpha_s'])" - ] - }, - { - "cell_type": "code", - "execution_count": 73, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "" - ] - }, - "execution_count": 73, + "execution_count": 11, "metadata": {}, "output_type": "execute_result" }, { "data": { - "image/png": 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"text/plain": [ "
" ] @@ -331,46 +220,8 @@ } ], "source": [ - "plt.plot(alpha, dic_alpha['lev_s'])\n", - "plt.axvline(dic_alpha['alpha_s'], color='red')" - ] - }, - { - "cell_type": "code", - "execution_count": 75, - "metadata": {}, - "outputs": [], - "source": [ - "new_p, new_std=reweight_alpha(alpha=dic_alpha['alpha_s'], samples=sampples)" - ] - }, - { - "cell_type": "code", - "execution_count": 76, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "(array([1391.19511519, 238.73263035, 1105.96237317, 1196.97269721,\n", - " 309.82950296, 1504.6730606 , 803.52558311, -120.1150033 ,\n", - " 712.445139 , 551.79621607, -168.6288367 , 206.4561598 ,\n", - " 354.3520938 , -81.88368176, 55.50049563, 275.65993193,\n", - " -48.13719587, 21.14055301]),\n", - " array([1394.82421048, 240.77213818, 1107.6120157 , 1196.74135383,\n", - " 309.03265131, 1505.47481376, 803.64908998, -120.54241659,\n", - " 712.86097633, 551.80037407, -168.58070723, 206.58579703,\n", - " 354.31364229, -81.88612007, 55.5125449 , 275.97669283,\n", - " -48.16602338, 21.14914733]))" - ] - }, - "execution_count": 76, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "new_p, flux_resample.maxlike.parameters_mean" + "plt.plot(flux_resample.maxlike.alpha, flux_resample.maxlike.best_alpha['lev_s'])\n", + "plt.axvline(flux_resample.maxlike.best_alpha['alpha_s'], color='red')" ] }, { diff --git a/sportran/md/maxlike.py b/sportran/md/maxlike.py index acd25ba..67fca04 100644 --- a/sportran/md/maxlike.py +++ b/sportran/md/maxlike.py @@ -420,7 +420,7 @@ def _store_optimization_results(self, res, write_log): """ Store the results of the optimization. """ - self.parameters_mean = res.x + if hasattr(res, "hess_inv"): cov = res.hess_inv if write_log: @@ -428,18 +428,35 @@ def _store_optimization_results(self, res, write_log): f"The {self.solver} solver provides Hessian. " "Covariance matrix estimated through Laplace approximation." ) - self.parameters_cov = cov - self.parameters_std = np.sqrt(cov.diagonal()) + + """ + Assume a gaussian prior (alpha/pi)**(P/2) e**(-alpha*||w||**2) and maximize the marginal distribution + of alpha. We sample the posterior distribution assuming it is Gaussian + (see https://en.wikipedia.org/wiki/Bernstein–von_Mises_theorem) and compute p(D|alpha) reweighting + the posterior at alpha=0: see reweight_alpha and reweight_logev_alpha_vec. + """ + + samples = generate_samples_mc_alpha(res.x, res.hess_inv) + + self.alpha = 10 ** (np.linspace(-10, -5, 10000)) + + dic_alpha = reweight_logev_alpha_vec(alpha=self.alpha, samples=samples) + + self.parameters_mean, self.parameters_cov = reweight_alpha(alpha=dic_alpha['alpha_s'], samples=samples) + + self.parameters_std = np.sqrt(self.parameters_cov.diagonal()) + self.best_alpha = dic_alpha else: if write_log: log.write_log( f"The {self.solver} solver does not provide Hessian. No covariance matrix output." ) + self.parameters_mean = res.x self.parameters_std = None self.optimizer_res = res self.log_likelihood_value = -self.log_like( - res.x, + self.parameters_mean, self.model, self.omega, self.omega_fixed, @@ -598,3 +615,43 @@ def scale_matrix_std_mc(model, w, omega, omega_fixed, n, cov_w, size=1000): ) S_std = sample_S.std(axis=0) return S_std + + +def reweight_logev_alpha_vec(samples, alpha): + ''' + samples: shape is (N, P): N number of samples, P number of parameters + array: array of alpha to test + ''' + M = samples.shape[1] + truth_mean = np.log(np.mean(np.exp(- alpha[:, None] * np.linalg.norm(samples, axis=1) ** 2), axis=1)) +\ + M / 2 * np.log(alpha * 2 / np.pi) + dic_alpha = {} + dic_alpha['lev_s'] = truth_mean + dic_alpha['alpha_s'] = alpha[np.argmax(dic_alpha['lev_s'])] + + + return dic_alpha + +def reweight_alpha(alpha, samples): + ''' + samples: shape is (N, P): N number of samples, P number of parameters + array: scalar + ''' + truth_mean = np.mean(samples.T[:, :] * np.exp(- alpha * np.linalg.norm(samples, axis=1) ** 2), axis=1) / \ + np.mean(np.exp(- alpha * np.linalg.norm(samples, axis=1) ** 2), axis=0) + truth_cov = np.mean(samples.T[:, None, :] * samples.T[None, :, :] * + np.exp(- alpha * np.linalg.norm(samples, axis=1) ** 2), axis=- 1) /\ + np.mean(np.exp(- alpha * np.linalg.norm(samples, axis=1) ** 2), axis=0) - \ + truth_mean[:, None]*truth_mean[None, :] + + return truth_mean, truth_cov + +def generate_samples_mc_alpha(w, cov_w, size=1000): + ''' + samples shape is (N, P): N number of samples, P number of parameters + w: parameters mean as estimated by self.maxlike + cov_w: array PxP + ''' + sample = w + np.random.multivariate_normal(mean=np.zeros_like(w), cov=cov_w, size=size) + + return sample