├── .gitignore ├── Chapter1 ├── README.md ├── answer.md ├── decision │ ├── images │ │ ├── class_conditional_densities.png │ │ ├── classification.png │ │ ├── loss_function_regression.png │ │ ├── loss_matrix.png │ │ ├── minkowski_loss.png │ │ └── reject_option.png │ ├── inference_decision.md │ ├── loss_function_regression.md │ ├── minimizing_expected_loss.md │ ├── minimizing_misclassification_rate.md │ └── reject_option.md ├── decision_theory.md ├── images │ ├── apple_orange.png │ ├── big_train.png │ ├── cross_validation.png │ ├── curse.png │ ├── divide_cell.png │ ├── entropy.png │ ├── fitting_example.png │ ├── handwrite.png │ ├── high_dim.png │ ├── high_dimensional_gaussian.png │ ├── regular.png │ ├── ridge.png │ ├── rms.png │ ├── rms_regular.png │ ├── sin.png │ ├── sum_of_square.png │ ├── table.png │ ├── two_random_variables.png │ ├── two_variables_distribute.png │ └── volume.png ├── information │ ├── images │ │ └── 1_31.png │ └── relative_entropy.md ├── information_theory.md ├── model_selection.md ├── polynomial_curve_fitting.md ├── probability │ ├── bayesian_curve_fitting.md │ ├── bayesian_probabilities.md │ ├── curve_fitting_revisited.md │ ├── expectations_covariances.md │ ├── gaussian_distribution.md │ ├── images │ │ ├── curve_gaussian.png │ │ ├── gaussian_distribution.png │ │ ├── gaussian_likehood.png │ │ ├── integration.png │ │ ├── likehood.png │ │ └── synthetic_sinusoidal.png │ └── probability_densities.md ├── probability_theory.md └── the_curse_of_dimensionality.md ├── Chapter10 ├── README.md ├── exceptation_propagation.md ├── exponential │ └── variational_message_passing.md ├── exponential_family.md ├── gaussian │ ├── components_number_determining.md │ ├── images │ │ ├── 10_6.png │ │ └── 10_7.png │ ├── induced_factorizations.md │ ├── predictive_density.md │ ├── variantiona_lower_bound.md │ └── variational_distribution.md ├── images │ ├── 10_10.png │ ├── 10_11.png │ ├── 10_12.png │ ├── 10_14.png │ ├── 10_5.png │ ├── 10_8.png │ └── approximation.png ├── linear │ ├── lower_bound.md │ ├── predictive_distribute.md │ └── variantional_distribution.md ├── local_variational_method.md ├── logistic │ ├── hyperparameter_inference.md │ ├── images │ │ ├── 10_13.png │ │ └── 10_14.png │ ├── optimization_variational_parameter.md │ └── variational_posterior_distribution.md ├── progagation │ ├── example_clutter.md │ ├── expection_propagation_graph.md │ └── images │ │ ├── 10_15.png │ │ ├── 10_16.png │ │ ├── 10_17.png │ │ └── 10_18.png ├── variational │ ├── example_univariate_gaussian.md │ ├── factorized_distributions.md │ ├── factorized_properties.md │ ├── images │ │ ├── 10_2.png │ │ ├── 10_3.png │ │ └── 10_4.png │ └── model_comparison.md ├── variational_inference.md ├── variational_linear_regression.md ├── variational_logistic_regression.md └── variational_mixture_gaussian.md ├── Chapter11 ├── README.md ├── basis │ ├── adaptive_rejection_sampling.md │ ├── images │ │ ├── 11_2.png │ │ ├── 11_3.png │ │ ├── 11_4.png │ │ ├── 11_5.png │ │ ├── 11_6.png │ │ └── 11_8.png │ ├── importance_sampling.md │ ├── rejection_sampling.md │ ├── sampling_em.md │ ├── sampling_importance_resampling.md │ └── standard_distribution.md ├── basis_sampling_algorithm.md ├── gibbs_sampling.md ├── hybrid_monte_carlo.md ├── images │ ├── 11_1.png │ ├── 11_11.png │ ├── 11_12.png │ ├── 11_13.png │ └── 11_9.png ├── markov │ ├── images │ │ └── 11_10.png │ ├── markob_chain.md │ └── metropolis_hastings.md ├── markov_chain_monte_carlo.md ├── monte │ ├── dynamical_systems.md │ ├── hybrid_monte_carlo.md │ └── images │ │ └── 11_14.png ├── partition_function_estimating.md └── slice_sampling.md ├── Chapter12 ├── README.md ├── images │ ├── 12_1.png │ ├── 12_16.png │ ├── 12_17.png │ ├── 12_2.png │ └── 12_9.png ├── kernel_pca.md ├── nolinear │ ├── autoassociative.md │ ├── images │ │ ├── 12_18.png │ │ ├── 12_19.png │ │ ├── 12_20.png │ │ └── 12_21.png │ ├── independent_component.md │ └── manifolds_modelling.md ├── nolinear_latent.md ├── pca │ ├── application.md │ ├── high_dimensional.md │ ├── images │ │ ├── 12_3.png │ │ ├── 12_4.png │ │ ├── 12_5.png │ │ ├── 12_6.png │ │ ├── 12_7.png │ │ └── 12_8.png │ ├── maximum_variance.md │ └── minimum_error.md ├── principal_component_analysis.md ├── probabilistic │ ├── bayesian.md │ ├── em.md │ ├── factor_analysis.md │ ├── images │ │ ├── 12_10.png │ │ ├── 12_13.png │ │ ├── 12_14.png │ │ └── 12_15.png │ └── maximum_likelihood.md └── probabilistic_pca.md ├── Chapter13 ├── README.md ├── hidden_markob_model.md ├── hmm │ ├── forward_backward.md │ ├── images │ │ ├── 13_12.png │ │ ├── 13_13.png │ │ ├── 13_14.png │ │ ├── 13_15.png │ │ ├── 13_16.png │ │ ├── 13_17.png │ │ ├── 13_18.png │ │ ├── 13_19.png │ │ └── 13_20.png │ ├── maimum_likelihood.md │ ├── markov_extensions.md │ ├── scaling_factors.md │ ├── sum_product.md │ └── viterbi.md ├── images │ ├── 13_1.png │ ├── 13_10.png │ ├── 13_11.png │ ├── 13_2.png │ ├── 13_3.png │ ├── 13_4.png │ ├── 13_5.png │ ├── 13_6.png │ ├── 13_7.png │ ├── 13_8.png │ └── 13_9.png ├── linear │ ├── images │ │ ├── 13_21.png │ │ ├── 13_22.png │ │ └── 13_23.png │ ├── lds_extensions.md │ ├── lds_inference.md │ ├── lds_learning.md │ └── particle_filters.md ├── linear_dynamical.md └── markob_model.md ├── Chapter14 ├── README.md ├── bayesian_model_avg.md ├── boosting.md ├── boosting │ ├── error_funcation.md │ ├── images │ │ ├── 14_3.png │ │ └── 14_4.png │ └── minimizing_exp_error.md ├── committees.md ├── conditional_mixture_models.md ├── images │ ├── 14_1.png │ ├── 14_10.png │ ├── 14_2.png │ ├── 14_5.png │ └── 14_6.png ├── logistic │ └── experts.md ├── logistic_mixture.md ├── mixture │ ├── images │ │ ├── 14_7.png │ │ ├── 14_8.png │ │ └── 14_9.png │ └── linear_regression.md └── tree_based_model.md ├── Chapter2 ├── README.md ├── binary │ ├── beta_distribute.md │ └── images │ │ ├── beta_distribution.png │ │ └── beta_step.png ├── binary_variables.md ├── exponential │ ├── conjugate_priors.md │ ├── maximum_likelihood.md │ └── noninformative_priors.md ├── gaussian │ ├── bayes_gaussian_variables.md │ ├── bayesian_inference_gaussian.md │ ├── conditional_gaussian_distributions.md │ ├── images │ │ ├── 2_10.png │ │ ├── 2_11.png │ │ ├── 2_17.png │ │ ├── a_function.png │ │ ├── bayesian_inference.png │ │ ├── bessel.png │ │ ├── conditional_marginal_gaussian.png │ │ ├── gamma.png │ │ ├── gaussian_contours.png │ │ ├── mixture_gaussian.png │ │ ├── mixture_gaussian_contour.png │ │ ├── normal_gaussian.png │ │ ├── old_faithful.png │ │ ├── t_distribution.png │ │ ├── t_gaussian_distribution.png │ │ └── von_mises.png │ ├── marginal_gaussian_distributions.md │ ├── maximum_likelihood_gaussian.md │ ├── mixtures_gaussian.md │ ├── periodic_variables.md │ ├── sequential_estimation.md │ └── student_t_distribution.md ├── images │ ├── binomal.png │ ├── cov_ellipse.png │ ├── elliptical.png │ ├── histogram_estimation.png │ └── sum_distribution.png ├── multinomial │ ├── dirichlet_distribute.md │ └── images │ │ ├── dirichlet.png │ │ └── simplex.png ├── multinomial_variables.md ├── nonparametric │ ├── images │ │ ├── 2_27_a.png │ │ ├── 2_27_b.png │ │ ├── k_nearest_neighbour.png │ │ ├── k_nearest_neighbour_classification.png │ │ ├── k_nearest_neighbour_oil.png │ │ └── kernel.png │ ├── kernel_density_estimators.md │ └── nearest_neighbour_method.md ├── nonparametric_method.md ├── the_exponential_family.md └── the_gaussian_distribution.md ├── Chapter3 ├── README.md ├── basis │ ├── geometry_least_square.md │ ├── images │ │ ├── lasso.png │ │ ├── least_sequares.png │ │ └── regularized.png │ ├── maximum_likelihood_least_square.md │ ├── multiple_outputs.md │ ├── regularized_least_squares.md │ └── sequential_learning.md ├── bayesian │ ├── equivalent_kernel.md │ ├── images │ │ ├── 3_10.png │ │ ├── 3_7.png │ │ ├── equivalent_kernel.png │ │ ├── funcation_sample.png │ │ └── sinusoidal.png │ ├── parameter_distribution.md │ └── predictive_distribution.md ├── bayesian_linear_regression.md ├── bayesian_model_comparison.md ├── bias_variance_decomposition.md ├── evidence │ ├── effective_number_parameter.md │ ├── evaluation_evidence_function.md │ ├── images │ │ ├── alpha_determine.png │ │ ├── contours.png │ │ ├── effective_parameter.png │ │ └── model_evidence.png │ └── maximizing_evidence_function.md ├── evidence_approximation.md ├── images │ ├── 3_1.png │ ├── bias_variance.png │ ├── fitting.png │ ├── model_approx.png │ └── schematic_illustration.png ├── limitations_fixed_basis_functions.md └── linear_basis_function.md ├── Chapter4 ├── README.md ├── bayesian │ ├── laplace.md │ └── predictive.md ├── bayesian_logistic_regression.md ├── discriminant │ ├── fisher_discriminant_multiple_classes.md │ ├── fisher_linear_discriminant.md │ ├── images │ │ ├── fisher.png │ │ ├── least_squares.png │ │ ├── least_squares_problem.png │ │ ├── one_rest.png │ │ ├── orientation_bias.png │ │ ├── perceptron.png │ │ ├── perceptron_machine.png │ │ └── two_points.png │ ├── least_squares.md │ ├── multiple_classes.md │ ├── perceptron_algorithm.md │ ├── relation_least_squares.md │ └── two_classes.md ├── discriminant_functions.md ├── images │ ├── laplace.png │ └── sigmoid.png ├── laplace │ └── model_comparison_bic.md ├── probabilistic │ ├── continuous_inputs.md │ ├── discrete_features.md │ ├── exponential_family.md │ ├── images │ │ ├── decision_boundary.png │ │ └── gaussian.png │ └── maximum_likelihood_solution.md ├── probabilistic_discriminant │ ├── canonical_link_functions.md │ ├── fixed_basis_functions.md │ ├── images │ │ ├── continuum.png │ │ └── correspond.png │ ├── iterative_reweighted_least_squares.md │ ├── logistic_regression.md │ ├── multiclass_logistic_regression.md │ └── probit_regression.md ├── probabilistic_discriminative_models.md ├── probabilistic_generative_model.md └── the_laplace_approximation.md ├── Chapter5 ├── README.md ├── backpropagation │ ├── efficiency_backpropagation.md │ ├── error_function_derivatives.md │ ├── images │ │ ├── arrangement.png │ │ └── jacobian.png │ ├── jacobian_matrix.md │ └── simple_example.md ├── bayesian │ ├── bayesian_network_classification.md │ ├── hyperparameter_optimization.md │ ├── images │ │ └── bayesian_classification.png │ └── posterior_parameter_distribution.md ├── bayesian_neural_networks.md ├── error_backpropagation.md ├── feed_forward_network_functions.md ├── forward │ └── weight_space_symmetries.md ├── hessian │ ├── diagonal_approximation.md │ ├── exact_evaluation_hessian.md │ ├── fast_multiplication_hessian.md │ ├── finite_differences.md │ ├── inverse_hessian.md │ └── outer_product_approximation.md ├── hessian_matrix.md ├── images │ ├── approximate.png │ ├── classification.png │ ├── feed_forward.png │ ├── m_effect.png │ ├── m_error.png │ ├── mixture_coefficient.png │ ├── mixture_dataset.png │ ├── mixture_density.png │ ├── network.png │ └── robot_arm.png ├── mixture_density_networks.md ├── network_training.md ├── regularization │ ├── consistent_gaussian_priors.md │ ├── convolutional_networks.md │ ├── early_stopping.md │ ├── images │ │ ├── approximation.png │ │ ├── convolutional.png │ │ ├── early_stopping.png │ │ ├── hyperparameter.png │ │ ├── number.png │ │ ├── similar.png │ │ └── sweep.png │ ├── invariances.md │ ├── soft_weight_sharing.md │ ├── tangent_propagation.md │ └── training_with_transformed_data.md ├── regularization_neural_networks.md └── training │ ├── gradient_descent_optimization.md │ ├── images │ └── contours.png │ ├── local_quadratic_approximation.md │ ├── parameter_optimization.md │ └── use_gradient_information.md ├── Chapter6 ├── README.md ├── constructing_kernels.md ├── dual_representations.md ├── gaussian │ ├── automatic_relevance_determination.md │ ├── connection_neural_networks.md │ ├── gaussian_processes_classification.md │ ├── gaussian_processes_regression.md │ ├── images │ │ ├── 6_8.png │ │ ├── ARD_prior.png │ │ ├── classification.png │ │ ├── gaussian_processes.png │ │ ├── gaussian_sample.png │ │ ├── laplace_approximation.png │ │ ├── principal.png │ │ ├── relevance.png │ │ └── theta_prior.png │ ├── laplace_approximation.md │ ├── learning_hyperparameters.md │ └── linear_regression_revisited.md ├── gaussian_processes.md ├── images │ ├── basis_function.png │ └── kernel_construction.png ├── radial │ ├── Nadaraya_Watson_model.md │ └── images │ │ └── nadaraya_watson_model.png └── radial_basis_funcation_networks.md ├── Chapter7 ├── README.md ├── images │ ├── margin.png │ └── margin_boundaries.png ├── margin │ ├── computational_learning_theory.md │ ├── images │ │ ├── epsilon_insensitive.png │ │ ├── hinge.png │ │ ├── slack_variables.png │ │ ├── svm_regression.png │ │ ├── v_SVM.png │ │ └── v_SVM_regression.png │ ├── logistic_regression_relation.md │ ├── multiclass_svm.md │ ├── overlapping_class_distributions.md │ └── svm_for_regression.md ├── maximum_margin_classifiers.md ├── relevance │ ├── analysis_sparsity.md │ ├── images │ │ ├── rvm_example.png │ │ ├── sparsity.png │ │ ├── svm_regression.png │ │ └── two_solution.png │ ├── rvm_classification.md │ └── rvm_for_regression.md └── relevance_vector_machines.md ├── Chapter8 ├── README.md ├── bayesian │ ├── discrete_variables.md │ ├── example_polynomial_regression.md │ ├── generative_models.md │ ├── images │ │ ├── directed_graphical.png │ │ ├── directed_graphical_compact.png │ │ ├── directed_graphical_determine.png │ │ ├── directed_graphical_observed.png │ │ ├── directed_graphical_probability.png │ │ ├── directed_graphical_regression.png │ │ ├── discrete.png │ │ ├── generative_models.png │ │ ├── model_extend.png │ │ ├── nodes_chain.png │ │ └── shared.png │ └── linear_gaussian_models.md ├── bayesian_network.md ├── conditional │ ├── d_separation.md │ ├── images │ │ ├── automobile.png │ │ ├── d_separation.png │ │ ├── df.png │ │ ├── first_three.png │ │ ├── first_three_conditional.png │ │ ├── gaussian.png │ │ ├── markov_blanket.png │ │ ├── navie_bayes.png │ │ ├── second_three.png │ │ ├── second_three_conditional.png │ │ ├── third_three.png │ │ └── third_three_conditional.png │ └── three_example_graphs.md ├── conditional_independence.md ├── images │ ├── bayes_graphical.png │ └── directed_acyclic_graphical.png ├── inference │ ├── factor_graph.md │ ├── images │ │ ├── chain.png │ │ ├── directed_factor_graph.png │ │ ├── directed_polytree.png │ │ ├── factor_graph.png │ │ ├── factor_sum_product.png │ │ ├── fragment.png │ │ ├── full_connect.png │ │ ├── messages.png │ │ ├── pure.png │ │ ├── subgraph.png │ │ ├── sum_product.png │ │ ├── table.png │ │ ├── trees.png │ │ ├── trellis.png │ │ └── undirected_factor_graph.png │ ├── inference_chain.md │ ├── inference_general_graph.md │ ├── learning_graph_structure.md │ ├── loopy_belief_propagation.md │ ├── max_sum_algorithm.md │ ├── sum_product_algorithm.md │ └── tree.md ├── inference_graphical_model.md ├── markov │ ├── conditional_independence_properities.md │ ├── factorization_properties.md │ ├── image_denoising.md │ ├── images │ │ ├── bayes_noise.png │ │ ├── equivalent.png │ │ ├── graphical.png │ │ ├── markov_blanket.png │ │ ├── moral_graph.png │ │ ├── undirected_36.png │ │ ├── undirected_conditional.png │ │ ├── undirected_graph.png │ │ └── venn.png │ └── relation_directed_graph.md └── markov_random_fields.md ├── Chapter9 ├── README.md ├── alternative │ ├── bayesian_regression_em.md │ ├── gaussian_mixture.md │ ├── images │ │ ├── discrete.png │ │ └── number.png │ ├── k_means_relation.md │ └── mixture_bernoulli.md ├── alternative_view_em.md ├── general_em.md ├── images │ ├── decomposition.png │ ├── e_step.png │ ├── em_parameter.png │ ├── k_old_faithful.png │ ├── m_step.png │ ├── mixture.png │ ├── mixture_gaussian.png │ └── old_faithful.png ├── k_means_clustering.md ├── means │ ├── image_segmentation_compression.md │ └── images │ │ └── image.png ├── mixture │ ├── em_gaussian.md │ ├── images │ │ ├── em_old_faithful.png │ │ ├── graph.png │ │ └── likelihood.png │ └── maximum_likelihood.md └── mixtures_gaussian.md ├── README.md ├── SUMMARY.md ├── _book ├── Chapter1 │ ├── decision │ │ └── images │ │ │ ├── class_conditional_densities.png │ │ │ ├── classification.png │ │ │ ├── loss_function_regression.png │ │ │ ├── loss_matrix.png │ │ │ ├── minkowski_loss.png │ │ │ └── reject_option.png │ ├── images │ │ ├── apple_orange.png │ │ ├── big_train.png │ │ ├── cross_validation.png │ │ ├── curse.png │ │ ├── divide_cell.png │ │ ├── entropy.png │ │ ├── fitting_example.png │ │ ├── handwrite.png │ │ ├── high_dim.png │ │ ├── high_dimensional_gaussian.png │ │ ├── regular.png │ │ ├── ridge.png │ │ ├── rms.png │ │ ├── rms_regular.png │ │ ├── sin.png │ │ ├── sum_of_square.png │ │ ├── table.png │ │ ├── two_random_variables.png │ │ ├── two_variables_distribute.png │ │ └── volume.png │ └── probability │ │ └── images │ │ ├── curve_gaussian.png │ │ ├── gaussian_distribution.png │ │ ├── gaussian_likehood.png │ │ ├── integration.png │ │ ├── likehood.png │ │ └── synthetic_sinusoidal.png └── Chapter2 │ ├── binary │ └── images │ │ ├── beta_distribution.png │ │ └── beta_step.png │ ├── gaussian │ └── images │ │ └── conditional_marginal_gaussian.png │ 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