Python pymc3.Uniform() Examples

def fit(self, X, Y, n_samples=10000, tune_steps=1000, n_jobs=4):
        with pm.Model() as self.model:
            # Priors
            std = pm.Uniform("std", 0, self.sps, testval=X.std())
            beta = pm.StudentT("beta", mu=0, lam=self.sps, nu=self.nu)
            alpha = pm.StudentT("alpha", mu=0, lam=self.sps, nu=self.nu, testval=Y.mean())
            # Deterministic model
            mean = pm.Deterministic("mean", alpha + beta * X)
            # Posterior distribution
            obs = pm.Normal("obs", mu=mean, sd=std, observed=Y)
            ## Run MCMC
            # Find search start value with maximum a posterior estimation
            start = pm.find_MAP()
            # sample posterior distribution for latent variables
            trace = pm.sample(n_samples, njobs=n_jobs, tune=tune_steps, start=start)
            # Recover posterior samples
            self.burned_trace = trace[int(n_samples / 2):] 

def ln_prob(self, sampler=None):
        """
        Change ln_prob method to take in a Sampler and return a PyMC3
        distribution.
        """

        from bilby.core.sampler import Pymc3

        if not isinstance(sampler, Pymc3):
            raise ValueError("Sampler is not a bilby Pymc3 sampler object")

        return pm.Uniform(self.name, lower=self.minimum,
                          upper=self.maximum)


# From hereon, the syntax is exactly equivalent to other bilby examples
# We make a prior 

def __init__(self):
        super(FlatSpec, self).__init__(testval=init.Uniform(1)) 

def fit(self, X, y):
        """
        Fits a Gaussian Process regressor using MCMC.

        Parameters
        ----------
        X: np.ndarray, shape=(nsamples, nfeatures)
            Training instances to fit the GP.
        y: np.ndarray, shape=(nsamples,)
            Corresponding continuous target values to `X`.

        """
        self.X = X
        self.n = self.X.shape[0]
        self.y = y
        self.model = pm.Model()

        with self.model as model:
            l = pm.Uniform('l', 0, 10)

            log_s2_f = pm.Uniform('log_s2_f', lower=-7, upper=5)
            s2_f = pm.Deterministic('sigmaf', tt.exp(log_s2_f))

            log_s2_n = pm.Uniform('log_s2_n', lower=-7, upper=5)
            s2_n = pm.Deterministic('sigman', tt.exp(log_s2_n))

            f_cov = s2_f * covariance_equivalence[type(self.covfunc).__name__](1, l)
            Sigma = f_cov(self.X) + tt.eye(self.n) * s2_n ** 2
            y_obs = pm.MvNormal('y_obs', mu=np.zeros(self.n), cov=Sigma, observed=self.y)
        with self.model as model:
            if self.step is not None:
                self.trace = pm.sample(self.niter, step=self.step())[self.burnin:]
            else:
                self.trace = pm.sample(self.niter, init=self.init)[self.burnin:] 

def fit(self, X, y):
        """
        Fits a Student-t regressor using MCMC.

        Parameters
        ----------
        X: np.ndarray, shape=(nsamples, nfeatures)
            Training instances to fit the GP.
        y: np.ndarray, shape=(nsamples,)
            Corresponding continuous target values to `X`.

        """
        self.X = X
        self.n = self.X.shape[0]
        self.y = y
        self.model = pm.Model()

        with self.model as model:
            l = pm.Uniform('l', 0, 10)

            log_s2_f = pm.Uniform('log_s2_f', lower=-7, upper=5)
            s2_f = pm.Deterministic('sigmaf', tt.exp(log_s2_f))

            log_s2_n = pm.Uniform('log_s2_n', lower=-7, upper=5)
            s2_n = pm.Deterministic('sigman', tt.exp(log_s2_n))

            f_cov = s2_f * covariance_equivalence[type(self.covfunc).__name__](1, l)
            Sigma = f_cov(self.X) + tt.eye(self.n) * s2_n ** 2
            y_obs = pm.MvStudentT('y_obs', nu=self.nu, mu=np.zeros(self.n), Sigma=Sigma, observed=self.y)
        with self.model as model:
            if self.step is not None:
                self.trace = pm.sample(self.niter, step=self.step())[self.burnin:]
            else:
                self.trace = pm.sample(self.niter, init=self.init)[self.burnin:] 

def sample(
            self, n_samples: int, beta: float = 1.):
        problem = self.problem
        log_post_fun = TheanoLogProbability(problem, beta)
        trace = self.trace

        x0 = None
        if self.x0 is not None:
            x0 = {x_name: val
                  for x_name, val in zip(self.problem.x_names, self.x0)}

        # create model context
        with pm.Model() as model:
            # uniform bounds
            k = [pm.Uniform(x_name, lower=lb, upper=ub)
                 for x_name, lb, ub in
                 zip(problem.get_reduced_vector(problem.x_names),
                     problem.lb, problem.ub)]

            # convert to tensor vector
            theta = tt.as_tensor_variable(k)

            # use a DensityDist for the log-posterior
            pm.DensityDist('log_post', logp=lambda v: log_post_fun(v),
                           observed={'v': theta})

            # step, by default automatically determined by pymc3
            step = None
            if self.step_function:
                step = self.step_function()

            # perform the actual sampling
            trace = pm.sample(
                draws=int(n_samples), trace=trace, start=x0, step=step,
                **self.options)

            # convert trace to inference data object
            data = az.from_pymc3(trace=trace, model=model)

        self.trace = trace
        self.data = data 

def __init__(self, minimum, maximum, name=None, latex_label=None):
        """
        Uniform prior with bounds (should be equivalent to bilby.prior.Uniform)
        """

        bilby.core.prior.Prior.__init__(self, name, latex_label,
                                        minimum=minimum,
                                        maximum=maximum) 

def __init__(
        self,
        learner_cls,
        parameter_keys,
        model_params,
        fit_params,
        model_path,
        **kwargs,
    ):
        self.priors = [
            [pm.Normal, {"mu": 0, "sd": 10}],
            [pm.Laplace, {"mu": 0, "b": 10}],
        ]
        self.uniform_prior = [pm.Uniform, {"lower": -20, "upper": 20}]
        self.prior_indices = np.arange(len(self.priors))
        self.parameter_f = [
            (pm.Normal, {"mu": 0, "sd": 5}),
            (pm.Cauchy, {"alpha": 0, "beta": 1}),
            0,
            -5,
            5,
        ]
        self.parameter_s = [
            (pm.HalfCauchy, {"beta": 1}),
            (pm.HalfNormal, {"sd": 0.5}),
            (pm.Exponential, {"lam": 0.5}),
            (pm.Uniform, {"lower": 1, "upper": 10}),
            10,
        ]
        # ,(pm.HalfCauchy, {'beta': 2}), (pm.HalfNormal, {'sd': 1}),(pm.Exponential, {'lam': 1.0})]
        self.learner_cls = learner_cls
        self.model_params = model_params
        self.fit_params = fit_params
        self.parameter_keys = parameter_keys
        self.parameters = list(product(self.parameter_f, self.parameter_s))
        pf_arange = np.arange(len(self.parameter_f))
        ps_arange = np.arange(len(self.parameter_s))
        self.parameter_ind = list(product(pf_arange, ps_arange))
        self.model_path = model_path
        self.models = dict()
        self.logger = logging.getLogger(ModelSelector.__name__) 

def construct_model(self, X, Y):
        """
            Constructs the nested logit model by applying priors on weight vectors **weights** as per :meth:`model_configuration`.
            Then we apply a uniform prior to the :math:`\\lambda s`, i.e. :math:`\\lambda s \\sim Uniform(\\text{alpha}, 1.0)`.
            The probability of choosing the object :math:`x_i` from the query set :math:`Q = \\{x_1, \\ldots ,x_n\\}` is
            evaluated in :meth:`get_probabilities`.

            Parameters
            ----------
            X : numpy array
                (n_instances, n_objects, n_features)
                Feature vectors of the objects
            Y : numpy array
                (n_instances, n_objects)
                Preferences in the form of discrete choices for given objects

            Returns
            -------
             model : pymc3 Model :class:`pm.Model`
        """
        self.loss_function_ = likelihood_dict.get(self.loss_function, None)
        with pm.Model() as self.model:
            self.Xt = theano.shared(X)
            self.Yt = theano.shared(Y)
            shapes = {"weights": self.n_object_features_fit_}
            weights_dict = create_weight_dictionary(self.model_configuration, shapes)
            lambda_k = pm.Uniform("lambda_k", self.alpha, 1.0, shape=self.n_nests)
            utility = tt.dot(self.Xt, weights_dict["weights"])
            self.p = self.get_probabilities(utility, lambda_k)
            LogLikelihood(
                "yl", loss_func=self.loss_function_, p=self.p, observed=self.Yt
            )
        self.logger.info("Model construction completed") 

def fit_cross_cov(self, n_exp=2, n_gauss=2, range_mu=None):
        """
        Fit an analytical covariance to the experimental data.
        Args:
            n_exp (int): number of exponential basic functions
            n_gauss (int): number of gaussian basic functions
            range_mu: prior mean of the range. Default mean of the lags

        Returns:
            pymc.Model: PyMC3 model to be sampled using MCMC
        """
        self.n_exp = n_exp
        self.n_gauss = n_gauss
        n_var = self.n_properties
        df = self.exp_var
        lags = self.lags

        # Prior standard deviation for the error of the regression
        prior_std_reg = df.std(0).max() * 10

        # Prior value for the mean of the ranges
        if not range_mu:
            range_mu = lags.mean()

        # pymc3 Model
        with pm.Model() as model:  # model specifications in PyMC3 are wrapped in a with-statement
            # Define priors
            sigma = pm.HalfCauchy('sigma', beta=prior_std_reg, testval=1., shape=n_var)

            psill = pm.Normal('sill', prior_std_reg, sd=.5 * prior_std_reg, shape=(n_exp + n_gauss))
            range_ = pm.Normal('range', range_mu, sd=range_mu * .3, shape=(n_exp + n_gauss))

            lambda_ = pm.Uniform('weights', 0, 1, shape=(n_var * (n_exp + n_gauss)))

            # Exponential covariance
            exp = pm.Deterministic('exp',
                                   # (lambda_[:n_exp*n_var]*
                                   psill[:n_exp] *
                                   (1. - T.exp(T.dot(-lags.values.reshape((len(lags), 1)),
                                                     (range_[:n_exp].reshape((1, n_exp)) / 3.) ** -1))))

            gauss = pm.Deterministic('gaus',
                                     psill[n_exp:] *
                                     (1. - T.exp(T.dot(-lags.values.reshape((len(lags), 1)) ** 2,
                                                       (range_[n_exp:].reshape((1, n_gauss)) * 4 / 7.) ** -2))))

            # We stack the basic functions in the same matrix and tile it to match the number of properties we have
            func = pm.Deterministic('func', T.tile(T.horizontal_stack(exp, gauss), (n_var, 1, 1)))

            # We weight each basic function and sum them
            func_w = pm.Deterministic("func_w", T.sum(func * lambda_.reshape((n_var, 1, (n_exp + n_gauss))), axis=2))

            for e, cross in enumerate(df.columns):
                # Likelihoods
                pm.Normal(cross + "_like", mu=func_w[e], sd=sigma[e], observed=df[cross].values)
        return model 

def fit_cross_cov(df, lags, n_exp=2, n_gaus=2, range_mu=None):
    n_var = df.columns.shape[0]
    n_basis_f = n_var * (n_exp + n_gaus)
    prior_std_reg = df.std(0).max() * 10
    #
    if not range_mu:
        range_mu = lags.mean()

    # Because is a experimental variogram I am not going to have outliers
    nugget_max = df.values.max()
    # print(n_basis_f, n_var*n_exp, nugget_max, range_mu, prior_std_reg)
    # pymc3 Model
    with pm.Model() as model:  # model specifications in PyMC3 are wrapped in a with-statement
        # Define priors
        sigma = pm.HalfCauchy('sigma', beta=prior_std_reg, testval=1., shape=n_var)

        psill = pm.Normal('sill', prior_std_reg, sd=.5 * prior_std_reg, shape=(n_exp + n_gaus))
        range_ = pm.Normal('range', range_mu, sd=range_mu * .3, shape=(n_exp + n_gaus))
        #  nugget = pm.Uniform('nugget', 0, nugget_max, shape=n_var)

        lambda_ = pm.Uniform('weights', 0, 1, shape=(n_var * (n_exp + n_gaus)))

        # Exponential covariance
        exp = pm.Deterministic('exp',
                               # (lambda_[:n_exp*n_var]*
                               psill[:n_exp] *
                               (1. - T.exp(T.dot(-lags.values.reshape((len(lags), 1)),
                                                 (range_[:n_exp].reshape((1, n_exp)) / 3.) ** -1))))

        gaus = pm.Deterministic('gaus',
                                psill[n_exp:] *
                                (1. - T.exp(T.dot(-lags.values.reshape((len(lags), 1)) ** 2,
                                                  (range_[n_exp:].reshape((1, n_gaus)) * 4 / 7.) ** -2))))

        func = pm.Deterministic('func', T.tile(T.horizontal_stack(exp, gaus), (n_var, 1, 1)))

        func_w = pm.Deterministic("func_w", T.sum(func * lambda_.reshape((n_var, 1, (n_exp + n_gaus))), axis=2))
        #           nugget.reshape((n_var,1)))

        for e, cross in enumerate(df.columns):
            # Likelihoods
            pm.Normal(cross + "_like", mu=func_w[e], sd=sigma[e], observed=df[cross].values)
    return model 

def construct_model(self, X, Y):
        """
            Constructs the nested logit model by applying priors on weight vectors **weights** and **weights_k** as per
            :meth:`model_configuration`. Then we apply a uniform prior to the :math:`\\lambda s`, i.e.
            :math:`\\lambda s \\sim Uniform(\\text{alpha}, 1.0)`.The probability of choosing the object :math:`x_i` from the
            query set :math:`Q = \\{x_1, \\ldots ,x_n\\}` is evaluated in :meth:`get_probabilities`.

            Parameters
            ----------
            X : numpy array
                (n_instances, n_objects, n_features)
                Feature vectors of the objects
            Y : numpy array
                (n_instances, n_objects)
                Preferences in the form of discrete choices for given objects

            Returns
            -------
             model : pymc3 Model :class:`pm.Model`
        """
        self.random_state_ = check_random_state(self.random_state)
        self.loss_function_ = likelihood_dict.get(self.loss_function, None)
        if np.prod(X.shape) > self.threshold:
            upper_bound = int(self.threshold / np.prod(X.shape[1:]))
            indices = self.random_state_.choice(X.shape[0], upper_bound, replace=False)
            X = X[indices, :, :]
            Y = Y[indices, :]
        self.logger.info(
            "Train Set instances {} objects {} features {}".format(*X.shape)
        )
        with pm.Model() as self.model:
            self.Xt = theano.shared(X)
            self.Yt = theano.shared(Y)
            shapes = {
                "weights": self.n_object_features_fit_,
                "weights_ik": (self.n_object_features_fit_, self.n_nests),
            }
            weights_dict = create_weight_dictionary(self.model_configuration, shapes)

            alpha_ik = tt.dot(self.Xt, weights_dict["weights_ik"])
            alpha_ik = ttu.softmax(alpha_ik, axis=2)
            utility = tt.dot(self.Xt, weights_dict["weights"])
            lambda_k = pm.Uniform("lambda_k", self.alpha, 1.0, shape=self.n_nests)
            self.p = self.get_probabilities(utility, lambda_k, alpha_ik)
            LogLikelihood(
                "yl", loss_func=self.loss_function_, p=self.p, observed=self.Yt
            )
        self.logger.info("Model construction completed") 

def fit(self, X, Y):
        model_args = dict()
        for param_key in self.parameter_keys:
            model_args[param_key] = self.uniform_prior
        self.logger.info("Uniform Prior")
        self.model_params["model_args"] = model_args
        key = "{}_uniform_prior".format(self.parameter_keys)
        self.fit_learner(X, Y, key)
        for j, param in enumerate(self.parameters):
            self.logger.info("mu: {}, sd/b: {}".format(*self.parameter_ind[j]))
            if len(self.parameter_keys) == 2:
                for i1, i2 in product(self.prior_indices, self.prior_indices):
                    prior1 = self.priors[i1]
                    prior2 = self.priors[i2]
                    self.logger.info("Priors {}, {}".format(i1, i2))
                    model_args = dict()
                    k1 = list(prior1[1].keys())
                    k2 = list(prior2[1].keys())
                    prior1[1] = dict(zip(k1, param))
                    prior2[1] = dict(zip(k2, param))
                    model_args[self.parameter_keys[0]] = prior1
                    model_args[self.parameter_keys[1]] = prior2
                    key = "{}_{}_{}_{}_mu_{}_sd_{}".format(
                        self.parameter_keys[0],
                        i1,
                        self.parameter_keys[1],
                        i2,
                        self.parameter_ind[j][0],
                        self.parameter_ind[j][1],
                    )
                    self.model_params["model_args"] = model_args
                    self.fit_learner(X, Y, key)
            else:
                for i, prior in enumerate(self.priors):
                    self.logger.info("Prior {}".format(i))
                    model_args = dict()
                    k1 = list(prior[1].keys())
                    prior[1] = dict(zip(k1, param))
                    model_args[self.parameter_keys[0]] = prior
                    self.model_params["model_args"] = model_args
                    key = "{}_{}_mu_{}_sd_{}".format(
                        self.parameter_keys[0],
                        i,
                        self.parameter_ind[j][0],
                        self.parameter_ind[j][1],
                    )
                    self.fit_learner(X, Y, key) 

def construct_model(self, X, Y):
        """
            Constructs the nested logit model by applying priors on weight vectors **weights** and **weights_k** as per
            :meth:`model_configuration`. Then we apply a uniform prior to the :math:`\\lambda s`, i.e.
            :math:`\\lambda s \\sim Uniform(\\text{alpha}, 1.0)`.The probability of choosing the object :math:`x_i` from
            the query set :math:`Q = \\{x_1, \\ldots ,x_n\\}` is evaluated in :meth:`get_probabilities`.

            Parameters
            ----------
            X : numpy array
                (n_instances, n_objects, n_features)
                Feature vectors of the objects
            Y : numpy array
                (n_instances, n_objects)
                Preferences in the form of discrete choices for given objects

            Returns
            -------
             model : pymc3 Model :class:`pm.Model`
        """
        self.loss_function_ = likelihood_dict.get(self.loss_function, None)
        if np.prod(X.shape) > self.threshold:
            upper_bound = int(self.threshold / np.prod(X.shape[1:]))
            indices = self.random_state_.choice(X.shape[0], upper_bound, replace=False)
            X = X[indices, :, :]
            Y = Y[indices, :]
        self.logger.info(
            "Train Set instances {} objects {} features {}".format(*X.shape)
        )
        y_nests = self.create_nests(X)
        with pm.Model() as self.model:
            self.Xt = theano.shared(X)
            self.Yt = theano.shared(Y)
            self.y_nests = theano.shared(y_nests)
            shapes = {
                "weights": self.n_object_features_fit_,
                "weights_k": self.n_object_features_fit_,
            }

            weights_dict = create_weight_dictionary(self.model_configuration, shapes)
            lambda_k = pm.Uniform("lambda_k", self.alpha, 1.0, shape=self.n_nests)
            weights = weights_dict["weights"] / lambda_k[:, None]
            utility = self._eval_utility(weights)
            utility_k = tt.dot(self.features_nests, weights_dict["weights_k"])
            self.p = self.get_probabilities(utility, lambda_k, utility_k)

            LogLikelihood(
                "yl", loss_func=self.loss_function_, p=self.p, observed=self.Yt
            )
        self.logger.info("Model construction completed")