Package: pydbm
Deep Learning Library: pydbmpydbmis Python library for building Restricted Boltzmann Machine(RBM), Deep Boltzmann Machine(DBM), Long Short-Term Memory Recurrent Temporal Restricted Boltzmann Machine(LSTM-RTRBM), and Shape Boltzmann Machine(Shape-BM). From the view points of functionally equivalents and structural expansions, this library also prototypes many variants such as Encoder/Decoder based on LSTM with an Attention mechanism, Convolutional Auto-Encoder, ConvLSTM, and Spatio-temporal Auto-Encoder.See also ...Automatic Summarization Library: pysummarizationIf you want to implement the Sequence-to-Sequence(Seq2Seq) model for the automatic summarization by usingpydbmto build the Encoder/Decoder controllers.Reinforcement Learning Library: pyqlearningIf you want to implement the Deep Reinforcement Learning, especially for Deep Q-Network and Multi-agent Deep Q-Network by usingpydbmas a Function Approximator.Generative Adversarial Networks Library: pyganIf you want to implement Generative Adversarial Networks(GANs) and Adversarial Auto-Encoders(AAEs) by usingpydbmas components for Generative models based on the Statistical machine learning problems.Algorithmic Composition or Automatic Composition Library: pycomposerIf you want to implement the Algorithmic Composer based on Generative Adversarial Networks(GANs) by usingpydbmandpyganas components for Generative models based on the Statistical machine learning problems.DocumentationFull documentation is available onhttps://code.accel-brain.com/Deep-Learning-by-means-of-Design-Pattern/. This document contains information on functionally reusability, functional scalability and functional extensibility.InstallationInstall using pip:pipinstall"git+https://github.com/chimera0/accel-brain-code.git#egg=pydbm&subdirectory=Deep-Learning-by-means-of-Design-Pattern"Or, after cloning this repository, you can install this library with the following command:gitclonehttps://github.com/chimera0/accel-brain-code.gitcdDeep-Learning-by-means-of-Design-Pattern/
pythonsetup.pybdist_wheel
pipinstalldist/pydbm-{version}-{hoge}.whlSource codeThe source code is currently hosted on GitHub.accel-brain-code/Deep-Learning-by-means-of-Design-PatternPython package index(PyPI)Installers for the latest released version are available at the Python package index.pydbm : Python Package IndexDependenciesnumpy: v1.13.3 or higher.cython: v0.27.1 or higher.OptionsPillow(PIL): v5.0.0 or higher.Only if you want to useImageGenerator.DescriptionThe function ofpydbmis building and modelingRestricted Boltzmann Machine(RBM) andDeep Boltzmann Machine(DBM). The models are functionally equivalent tostacked auto-encoder. The basic function is the same asdimensions reduction(orpre-learning). And this library enables you to build many functional extensions from RBM and DBM such as Recurrent Temporal Restricted Boltzmann Machine(RTRBM), Recurrent Neural Network Restricted Boltzmann Machine(RNN-RBM), Long Short-Term Memory Recurrent Temporal Restricted Boltzmann Machine(LSTM-RTRBM), and Shape Boltzmann Machine(Shape-BM).As more usecases,RTRBM,RNN-RBM, andLSTM-RTRBMcan learn dependency structures in temporal patterns such as music, natural sentences, and n-gram. RTRBM is a probabilistic time-series model which can be viewed as a temporal stack of RBMs, where each RBM has a contextual hidden state that is received from the previous RBM and is used to modulate its hidden units bias. The RTRBM can be understood as a sequence of conditional RBMs whose parameters are the output of a deterministic RNN, with the constraint that the hidden units must describe the conditional distributions. This constraint can be lifted by combining a full RNN with distinct hidden units. In terms of this possibility, RNN-RBM and LSTM-RTRBM are structurally expanded model from RTRBM that allows more freedom to describe the temporal dependencies involved.The usecases ofShape-BMare image segmentation, object detection, inpainting and graphics. Shape-BM is the model for the task of modeling binary shape images, in that samples from the model look realistic and it can generalize to generate samples that differ from training examples.Image inthe Weizmann horse dataset.Binarized image.Reconstructed image by Shape-BM.The structure of RBM.According to graph theory, the structure of RBM corresponds to a complete bipartite graph which is a special kind of bipartite graph where every node in the visible layer is connected to every node in the hidden layer. Based on statistical mechanics and thermodynamics(Ackley, D. H., Hinton, G. E., & Sejnowski, T. J. 1985), the state of this structure can be reflected by the energy function:whereis a bias in visible layer,is a bias in hidden layer,is an activity or a state in visible layer,is an activity or a state in hidden layer, andis a weight matrix in visible and hidden layer. The activities can be calculated as the below product, since the link of activations of visible layer and hidden layer are conditionally independent.The learning equations of RBM.Because of the rules of conditional independence, the learning equations of RBM can be introduced as simple form. The distribution of visible statewhich is marginalized over the hidden stateis as following:whereis a partition function in statistical mechanics or thermodynamics. Letbe set of observed data points, then. Therefore the gradients on the parameterof the log-likelihood function arewhereis an expected value for.is a sigmoid function.The learning equations of RBM are introduced by performing control so that those gradients can become zero.Contrastive Divergence as an approximation method.In relation to RBM,Contrastive Divergence(CD) is a method for approximation of the gradients of the log-likelihood(Hinton, G. E. 2002). The procedure of this method is similar to Markov Chain Monte Carlo method(MCMC). However, unlike MCMC, the visbile variables to be set first in visible layer is not randomly initialized but the observed data points in training dataset are set to the first visbile variables. And, like Gibbs sampler, drawing samples from hidden variables and visible variables is repeatedktimes. Empirically (and surprisingly),kis considered to be1.The structure of DBM.Salakhutdinov, R., Hinton, G. E. (2009). Deep boltzmann machines. In International conference on artificial intelligence and statistics (pp. 448-455). p451.As is well known, DBM is composed of layers of RBMs stacked on top of each other(Salakhutdinov, R., & Hinton, G. E. 2009). This model is a structural expansion of Deep Belief Networks(DBN), which is known as one of the earliest models of Deep Learning(Le Roux, N., & Bengio, Y. 2008). Like RBM, DBN places nodes in layers. However, only the uppermost layer is composed of undirected edges, and the other consists of directed edges. DBN withRhidden layers is below probabilistic model:wherer = 0points to visible layer. Considerling simultaneous distribution in top two layer,and conditional distributions in other layers are as follows:The pre-learning of DBN engages in a procedure of recursive learning in layer-by-layer. However, as you can see from the difference of graph structure, DBM is slightly different from DBN in the form of pre-learning. For instance, ifr = 1, the conditional distribution of visible layer is.On the other hand, the conditional distribution in the intermediate layer iswhere2has been introduced considering that the intermediate layerrreceives input data from Shallower layerr-1and deeper layerr+1. DBM sets these parameters as initial states.DBM as a Stacked Auto-Encoder.DBM is functionally equivalent to aStacked Auto-Encoder, which is-a neural network that tries to reconstruct its input. Toencodethe observed data points, the function of DBM is as linear transformation of feature map below.On the other hand, todecodethis feature points, the function of DBM is as linear transformation of feature map below.The reconstruction error should be calculated in relation to problem setting. This library provides a default method, which can be overridden, for error function that computes Mean Squared Error(MSE). For instance, my jupyter notebook:demo/demo_stacked_auto_encoder.ipynbdemonstrates the reconstruction errors of DBM which is a Stacked Auto-Encoder.Structural expansion for RTRBM.TheRTRBM(Sutskever, I., et al. 2009) is a probabilistic time-series model which can be viewed as a temporal stack of RBMs, where each RBM has a contextual hidden state that is received from the previous RBM and is used to modulate its hidden units bias. Letbe the hidden state in previous stept-1. The conditional distribution in hidden layer in timetiswhereis weight matrix in each time steps. Then sampling of observed data points is is as following:While the hidden units are binary during inference and sampling, it is the mean-field valuethat is transmitted to its successors.Structural expansion for RNN-RBM.The RTRBM can be understood as a sequence of conditional RBMs whose parameters are the output of a deterministic RNN, with the constraint that the hidden units must describe the conditional distributions and convey temporal information. This constraint can be lifted by combining a full RNN with distinct hidden units.RNN-RBM(Boulanger-Lewandowski, N., et al. 2012), which is the more structural expansion of RTRBM, has also hidden units.Boulanger-Lewandowski, N., Bengio, Y., & Vincent, P. (2012). Modeling temporal dependencies in high-dimensional sequences: Application to polyphonic music generation and transcription. arXiv preprint arXiv:1206.6392., p4.Single arrows represent a deterministic function, double arrows represent the stochastic hidden-visible connections of an RBM.The biases are linear function of. This hidden units are only connected to their direct predecessorand visible units in timetby the relation:whereandare weight matrixes.Structural expansion for LSTM-RTRBM.An example of the application to polyphonic music generation(Lyu, Q., et al. 2015) clued me in on how is it possible to connect RTRBM with LSTM.Structure of LSTM.Originally, Long Short-Term Memory(LSTM) networks as a special RNN structure has proven stable and
powerful for modeling long-range dependencies. The Key point of structural expansion is its memory cellwhich essentially acts as an accumulator of the state information. Every time observed data points are given as new informationand input to LSTM's input gate, its information will be accumulated to the cell if the input gateis activated. The past state of cellcould be forgotten in this process if LSTM's forget gateis on. Whether the latest cell outputwill be propagated to the final stateis further controlled by the output gate.Omitting so-called peephole connection, it makes possible to combine the activations in LSTM gates into an affine transformation below.whereis a weight matrix which connects observed data points and hidden units in LSTM gates, andis a weight matrix which connects hidden units as a remembered memory in LSTM gates. Furthermore, activation functions are as follows:and the acitivation of memory cell and hidden units are calculated as follows:Structure of LSTM-RTRBM.LSTM-RTRBMmodel integrates the ability of LSTM in memorizing and retrieving useful history information, together with the advantage of RBM in high dimensional data modelling(Lyu, Q., Wu, Z., Zhu, J., & Meng, H. 2015, June). Like RTRBM, LSTM-RTRBM also has the recurrent hidden units. Letbe previous hidden units. The conditional distribution of the current hidden layer is as following:whereis a weight matrix which indicates the connectivity between states at each time step in RBM. Now, sampling the observed data pointsin RTRBM is as follows."Adding LSTM units to RTRBM is not trivial, considering RTRBM’s hidden units and visible units are intertwined in inference and learning. The simplest way to circumvent this difficulty is to use bypass connections from LSTM units to the hidden units besides the existing recurrent connections of hidden units, as in LSTM-RTRBM."Lyu, Q., Wu, Z., & Zhu, J. (2015, October). Polyphonic music modelling with LSTM-RTRBM. In Proceedings of the 23rd ACM international conference on Multimedia (pp. 991-994). ACM., p.993.Therefore it is useful to introduce a distinction ofchannelwhich means the sequential information.indicates the direct connectivity in RBM, whilecan be defined as a concept representing the previous time step combination in the LSTM units. Letandbe the hidden units indicating short-term memory and long-term memory, respectively. Then sampling the observed data pointsin LSTM-RTRBM can be re-described as follows.Structural expansion for Shape-BM.The concept ofShape Boltzmann Machine(Eslami, S. A., et al. 2014) provided inspiration to this library. This model uses below has two layers of hidden variables:and. The visible unitsvarethe pixels of a binary image of size. In the visible layer we enforce local receptive fields by connecting each hidden unit inonly to a subset of the visible units, corresponding to one of four rectangular patches. In order to encourage boundary consistency each patch overlaps its neighbor bypixels and so has side lengths ofand. In this model, the weight matrix in visible and hidden layer correspond to conectivity between the four sets of hidden units and patches, however the visible biasesare not shared.Eslami, S. A., Heess, N., Williams, C. K., & Winn, J. (2014). The shape boltzmann machine: a strong model of object shape. International Journal of Computer Vision, 107(2), 155-176., p156.Eslami, S. A., Heess, N., Williams, C. K., & Winn, J. (2014). The shape boltzmann machine: a strong model of object shape. International Journal of Computer Vision, 107(2), 155-176., p156.The Shape-BM is a DBM in three layer. The learning algorithm can be completed by optimization ofwhere.The Commonality/Variability Analysis in order to practice object-oriented design.From perspective ofcommonality/variability analysisin order to practice object-oriented design, the concepts of RBM and DBM paradigms can be organized as follows:Pay attention to the interface of the above class diagram. While each model iscommonin that it is constituted by stacked RBM, its approximation methods and activation functions arevariabledepending on the problem settings.Considering thecommonality, it is useful to design based onBuilder Patternrepresented byDBMBuilderorRTRBMBuilder, which separates the construction of RBM objectRestrictedBoltzmannMachinefrom its representation byDBMDirectororRTRBMDirectorso that the same construction process can create different representations such as DBM, RTRBM, RNN-RBM, and Shape-BM. Additionally, the models of all neural networks arecommonin that they possess like synapses by obtaining computation graphs without exception. So the classSynapseis contained in various models in a state where computation graphs of weight matrix and bias vector are held in the field.On the other hand, to deal with thevariability,Strategy Pattern, which provides a way to define a family of algorithms such as approximation methods implemented by inheriting the interfaceApproximateInterface, and also activation functions implemented by inheriting the interfaceActivatingFunctionInterface, is useful design method, which is encapsulate each one as an object, and make them interchangeable from the point of view of functionally equivalent.Template Method Patternis also useful design method to design the optimizer in this library because this design pattern makes it possible to define the skeleton of an algorithm in a parameter tuning, deferring some steps to client subclasses such asSGD,AdaGrad,RMSProp,NAG,AdamorNadam. Template Method lets subclasses redefine certain steps of an algorithm without changing the algorithm’s structure.Functionally equivalent: Encoder/Decoder based on LSTM.The methodology ofequivalent-functionalismenables us to introduce more functional equivalents and compare problem solutions structured with different algorithms and models in common problem setting. For example, in dimension reduction problem, the function ofEncoder/Decoder schemais equivalent toDBMas aStacked Auto-Encoder.Cho, K., Van Merriënboer, B., Gulcehre, C., Bahdanau, D., Bougares, F., Schwenk, H., & Bengio, Y. (2014). Learning phrase representations using RNN encoder-decoder for statistical machine translation. arXiv preprint arXiv:1406.1078., p2.According to the neural networks theory, and in relation to manifold hypothesis, it is well known that multilayer neural networks can learn features of observed data points and have the feature points in hidden layer. High-dimensional data can be converted to low-dimensional codes by training the model such asStacked Auto-EncoderandEncoder/Decoderwith a small central layer to reconstruct high-dimensional input vectors. This function of dimensionality reduction facilitates feature expressions to calculate similarity of each data point.This library providesEncoder/Decoder based on LSTM, which is a reconstruction model and makes it possible to extract series features embedded in deeper layers. The LSTM encoder learns a fixed length vector of time-series observed data points and the LSTM decoder uses this representation to reconstruct the time-series using the current hidden state and the value inferenced at the previous time-step.As in the above class diagram, in this library, the classEncoderDecoderControllercan be composed of twoLSTMModels.LSTMModelis-aReconstructableModel, which has a learning method and an inference method like the ordinary supervised learning model.An example is illustrated in this my jupyter notebook:demo/demo_sine_wave_prediction_by_LSTM_encoder_decoder.ipynb. This notebook demonstrates a simple sine wave prediction by Encoder/Decoder based on LSTM.Encoder/Decoder for Anomaly Detection(EncDec-AD)One interesting application example is theEncoder/Decoder for Anomaly Detection (EncDec-AD)paradigm (Malhotra, P., et al. 2016). This reconstruction model learns to reconstructnormaltime-series behavior, and thereafter uses reconstruction error to detect anomalies. Malhotra, P., et al. (2016) showed that EncDec-AD paradigm is robust and can detect anomalies from predictable, unpredictable, periodic, aperiodic, and quasi-periodic time-series. Further, they showed that the paradigm is able to detect anomalies from short time-series (length as small as 30) as well as long time-series (length as large as 500).As the prototype is exemplified indemo/demo_anomaly_detection_by_enc_dec_ad.ipynb, this library provides Encoder/Decoder based on LSTM as a EncDec-AD scheme.Functionally equivalent: Convolutional Auto-Encoder.Shape-BMis a kind of problem solution in relation to problem settings such as image segmentation, object detection, inpainting and graphics. In this problem settings,Convolutional Auto-Encoder(Masci, J., et al., 2011) is a functionally equivalent ofShape-BM. A stack of Convolutional Auto-Encoder forms a convolutional neural network(CNN), which are among the most successful models for supervised image classification. Each Convolutional Auto-Encoder is trained using conventional on-line gradient descent without additional regularization terms.Image inthe Weizmann horse dataset.Reconstructed image byShape-BM.Reconstructed image byConvolutional Auto-Encoder.My jupyter notebook:demo/demo_convolutional_auto_encoder.ipynbalso demonstrates various reconstructed images.This library can draw a distinction betweenStacked Auto-EncoderandConvolutional Auto-Encoder, and is able to design and implement respective models.Stacked Auto-Encoderignores the 2 dimentional image structures. In many cases, the rank of observed tensors extracted from image dataset is more than 3. This is not only a problem when dealing with realistically sized inputs, but also introduces redundancy in the parameters, forcing each feature to be global. LikeShape-BM,Convolutional Auto-Encoderdiffers fromStacked Auto-Encoderas their weights are shared among all locations in the input, preserving spatial locality. Hence, the reconstructed image data is due to a linear combination of basic image patches based on the latent code.In this library,Convolutional Auto-Encoderis also based onEncoder/Decoderscheme. Theencoderis to thedecoderwhat theConvolutionis to theDeconvolution. The Deconvolution also called transposed convolutions "work by swapping the forward and backward passes of a convolution." (Dumoulin, V., & Visin, F. 2016, p20.)Structural expansion for Convolutional LSTM(ConvLSTM).Convolutional LSTM(ConvLSTM)(Xingjian, S. H. I. et al., 2015), which is a model that structurally couplesconvolution operatorstoLSTMnetworks, can be utilized as components in constructing the Encoder/Decoder. The ConvLSTM is suitable for spatio-temporal data due to its inherent convolutional structure.Xingjian, S. H. I., Chen, Z., Wang, H., Yeung, D. Y., Wong, W. K., & Woo, W. C. (2015). Convolutional LSTM network: A machine learning approach for precipitation nowcasting. In Advances in neural information processing systems (pp. 802-810), p806.This library also makes it possible to buildEncoder/Decoder based on ConvLSTM. My jupyter notebook:demo/demo_conv_lstm.ipynbdemonstrates that the Encoder/Decoder based on Convolutional LSTM(ConvLSTM) can learn images and reconstruct its.Structural expansion for Spatio-Temporal Auto-Encoder.Encoder/Decoder based on ConvLSTMandConvolutional Auto-Encoderhave a functional reusability to extend the structures toSpatio-Temporal Auto-Encoder, which can learn the regular patterns in the training videos(Baccouche, M., et al., 2012, Patraucean, V., et al. 2015). This model consists of spatial Auto-Encoder and temporal Encoder/Decoder. The spatial Auto-Encoder is a Convolutional Auto-Encoder for learning spatial structures of each video frame. The temporal Encoder/Decoder is an Encoder/Decoder based on LSTM scheme for learning temporal patterns of the encoded spatial structures. The spatial encoder and decoder have two convolutional and deconvolutional layers respectively, while the temporal encoder and decoder are to act as a twin LSTM models.Chong, Y. S., & Tay, Y. H. (2017, June). Abnormal event detection in videos using spatiotemporal autoencoder. In International Symposium on Neural Networks (pp. 189-196). Springer, Cham., p.195.Because of the structural expansions,ConvLSTMandSpatio-Temporal Auto-Encodercan be consisted bycnnsubpackage, which is responsible for convolution and deconvolution of spatial features, andrnnsubpackage for controlling reconstruction of temporal features as in the following class diagram.Incnnsubpackage, the classLayerableCNNis an abstract class to implement CNN layers such asConvolutionLayerandMaxPoolingLayer.ConvolutionalAutoEncoderandSpatioTemporalAutoEncoderhave those CNN layers, especiallyConvolutionLayerto convolve as forward propagation and to deconvolve as back propagation, and are common in the sense that each class has a learning method and an inference method. The difference is that onlySpatioTemporalAutoEncoderis related toReconstructableModelsuch asLSTMModelandConvLSTMModelinrnnsubpackage.Video recognition and reconstruction of video images.demo/demo_spatio_temporal_auto_encoder.ipynbis a jupyter notebook which demonstrates the video recognition and reconstruction of video images by the Spatio-Temporal Auto-Encoder.Structural extension from Auto-Encoders and Encoder/Decoders to energy-based models and Generative models.Auto-Encoders, such as the Convolutional Auto-Encoder, the Spatio-Temporal Auto-Encoder, and the DBM have in common that these models are Stacked Auto-Encoders. And the Encoder/Decoder based on LSTM or ConvLSTM share similarity with the RTRBM, RNN-RBM, and LSTM-RTRBM, as the reconstruction models. On the other hand, the Auto-Encoders and the Encoder/Decoders are not statistical mechanical energy-based models unlike with RBM or DBM.However, Auto-Encoders have traditionally been used to represent energy-based models. According to the statistical mechanical theory for energy-based models, Auto-Encoders constructed by neural networks can be associated with an energy landscape, akin to negative log-probability in a probabilistic model, which measures how well the Auto-Encoder can represent regions in the input space. The energy landscape has been commonly inferred heuristically, by using a training criterion that relates the Auto-Encoder to a probabilistic model such as a RBM. The energy function is identical to the free energy of the corresponding RBM, showing that Auto-Encoders and RBMs may be viewed as two different ways to derive training criteria for forming the same type of analytically defined energy landscape.The view of the Auto-Encoder as a dynamical system allows us to understand how an energy function may be derived for the Auto-Encoder. This makes it possible to assign energies to Auto-Encoders with many different types of activation functions and outputs, and consider minimanization of reconstruction errors as energy minimanization(Kamyshanska, H., & Memisevic, R., 2014).When trained with some regularization terms, the Auto-Encoders have the ability to learn an energy manifold without supervision or negative examples(Zhao, J., et al., 2016). This means that even when an energy-based Auto-Encoding model is trained to reconstruct a real sample, the model contributes to discovering the data manifold by itself.This library provides energy-based Auto-Encoders such as Contractive Convolutional Auto-Encoder(Rifai, S., et al., 2011), Repelling Convolutional Auto-Encoder(Zhao, J., et al., 2016), Denoising Auto-Encoders(Bengio, Y., et al., 2013), and Ladder Networks(Valpola, H., 2015). But it is more usefull to redescribe the Auto-Encoders in the framework of Generative Adversarial Networks(GANs)(Goodfellow, I., et al., 2014) to make those models function as not only energy-based models but also Generative models. For instance, theory of an Adversarial Auto-Encoders(AAEs)(Makhzani, A., et al., 2015) and energy-based GANs(EBGANs)(Zhao, J., et al., 2016) enables us to turn Auto-Encoders into a Generative models which referes energy functions. If you want to implement GANs and AAEs by usingpydbmas components for Generative models based on the Statistical machine learning problems, seeGenerative Adversarial Networks Library: pygan.Composition and Correspondence in this libraryTo summarize the information so far into one class diagram, the outline is as follows.Unlikedbmsubpackage,rnnsubpackage andcnnsubpackage have an association with the interfaceComputableLoss. The subclass are Loss functions such as Mean Square Error(MSE) and Cross Entropy. Thefunctionof loss functions fordbmis included in thefunctionof energy functions optimized to minimize cost in the interfaceApproximateInterface.Usecase: Building the Deep Boltzmann Machine for feature extracting.Import Python and Cython modules based on Builder Pattern.# The `Client` in Builder Patternfrompydbm.dbm.deep_boltzmann_machineimportDeepBoltzmannMachine# The `Concrete Builder` in Builder Pattern.frompydbm.dbm.builders.dbm_multi_layer_builderimportDBMMultiLayerBuilder# Contrastive Divergence for function approximation.frompydbm.approximation.contrastive_divergenceimportContrastiveDivergenceImport Python and Cython modules of activation functions.# Logistic Function as activation function.frompydbm.activation.logistic_functionimportLogisticFunction# Tanh Function as activation function.frompydbm.activation.tanh_functionimportTanhFunction# ReLu Function as activation function.frompydbm.activation.relu_functionimportReLuFunctionImport Python and Cython modules of optimizers, and instantiate the objects.# Stochastic Gradient Descent(SGD) as optimizer.frompydbm.optimization.optparams.sgdimportSGD# is-a `OptParams`.opt_params=SGD(# Momentum.momentum=0.9)If you want to use not Stochastic Gradient Descent(SGD) but Adam(Kingma, D. P., & Ba, J., 2014) optimizer, importAdamand instantiate it.# Adam as a optimizer.frompydbm.optimization.optparams.adamimportAdam# is-a `OptParams`.opt_params=Adam(# BETA 1.beta_1=0.9,# BETA 2.beta_2=0.99)Setup parameters of regularization. For instance, constraining (or scale down) weight vectors and the probability of dropout(Srivastava, N., Hinton, G., et al., 2014, Zaremba, W., et al., 2014) can be set as follows.# Regularization for weights matrix# to repeat multiplying the weights matrix and `0.9`# until $\sum_{j=0}^{n}w_{ji}^2 < weight\_limit$.opt_params.weight_limit=1e+03# Probability of dropout.opt_params.dropout_rate=0.5Instantiate objects and call the method.# Contrastive Divergence for visible layer and first hidden layer.first_cd=ContrastiveDivergence(opt_params=opt_params)# Contrastive Divergence for first hidden layer and second hidden layer.second_cd=ContrastiveDivergence(opt_params=opt_params)# DBMdbm=DeepBoltzmannMachine(# `Concrete Builder` in Builder Pattern,# which composes three restricted boltzmann machines for building a deep boltzmann machine.DBMMultiLayerBuilder(),# Dimention in visible layer, hidden layer, and second hidden layer.[train_arr.shape[1],10,train_arr.shape[1]],# Setting objects for activation function.[ReLuFunction(),LogisticFunction(),TanhFunction()],# Setting the object for function approximation.[first_cd,second_cd],# Setting learning rate.learning_rate=0.05)# Execute learning.dbm.learn(# `np.ndarray` of observed data points.train_arr,# If approximation is the Contrastive Divergence, this parameter is `k` in CD method.training_count=1,# Batch size in mini-batch training.batch_size=200,# if `r_batch_size` > 0, the function of `dbm.learn` is a kind of reccursive learning.r_batch_size=-1)If you do not want to execute the mini-batch training, the value ofbatch_sizemust be-1. Andr_batch_sizeis also parameter to control the mini-batch training but is refered only in inference and reconstruction. If this value is more than0,  the inferencing is a kind of reccursive learning with the mini-batch training.And the feature points can be extracted by this method.feature_point_arr=dbm.get_feature_point(layer_number=1)Usecase: Extracting all feature points for dimensions reduction(or pre-learning)Import Python and Cython modules and instantiate the objects in the same manner asUsecase: Building the Deep Boltzmann Machine for feature extracting.Import and instantiate notDeepBoltzmannMachinebutStackedAutoEncoder, and call the method.# `StackedAutoEncoder` is-a `DeepBoltzmannMachine`.frompydbm.dbm.deepboltzmannmachine.stacked_auto_encoderimportStackedAutoEncoder# is-a `DeepBoltzmannMachine`.dbm=StackedAutoEncoder(DBMMultiLayerBuilder(),[target_arr.shape[1],10,target_arr.shape[1]],activation_list,approximaion_list,learning_rate=0.05# Setting learning rate.)# Execute learning.dbm.learn(target_arr,1,# If approximation is the Contrastive Divergence, this parameter is `k` in CD method.batch_size=200,# Batch size in mini-batch training.r_batch_size=-1# if `r_batch_size` > 0, the function of `dbm.learn` is a kind of reccursive learning.)The function ofcomputable_lossis computing the reconstruction error.MeanSquaredErroris-aComputableLoss, which is so-called Loss function.Extract reconstruction error rate.You can check the reconstruction error rate. During the approximation of the Contrastive Divergence, the mean squared error(MSE) between the observed data points and the activities in visible layer is computed as the reconstruction error rate.Callget_reconstruct_error_arrmethod as follow.reconstruct_error_arr=dbm.get_reconstruct_error_arr(layer_number=0)layer_numbercorresponds to the index ofapproximaion_list. Andreconstruct_error_arris thenp.ndarrayof reconstruction error rates.Extract the result of dimention reductionAnd the result of dimention reduction can be extracted by this property.pre_learned_arr=dbm.feature_points_arrExtract weights obtained by pre-learning.If you want to get the pre-learning weights, callget_weight_arr_listmethod.weight_arr_list=dbm.get_weight_arr_list()weight_arr_listis thelistof weights of each links in DBM.weight_arr_list[0]is 2-dnp.ndarrayof weights between visible layer and first hidden layer.Extract biases obtained by pre-learning.Callget_visible_bias_arr_listmethod andget_hidden_bias_arr_listmethod in the same way.visible_bias_arr_list=dbm.get_visible_bias_arr_list()hidden_bias_arr_list=dbm.get_hidden_bias_arr_list()visible_bias_arr_listandhidden_bias_arr_listare thelistof biases of each links in DBM.Save pre-learned parameters.The objectdbm, which is-aDeepBoltzmannMachine, has the methodsave_pre_learned_params, to store the pre-learned parameters in compressedNPY formatfiles.# Save pre-learned parameters.dbm.save_pre_learned_params(# Path of dir. If `None`, the file is saved in the current directory.dir_path="/var/tmp/",# The naming rule of files. If `None`, this value is `dbm`.file_name="demo_dbm")Transfer learning in DBM.DBMMultiLayerBuildercan be givenpre_learned_path_listwhich is alistof file paths that store pre-learned parameters.dbm=StackedAutoEncoder(DBMMultiLayerBuilder(# `list` of file path that stores pre-learned parameters.pre_learned_path_list=["/var/tmp/demo_dbm_0.npz","/var/tmp/demo_dbm_1.npz"]),[next_target_arr.shape[1],10,next_target_arr.shape[1]],activation_list,approximaion_list,# Setting learning rate.0.05)# Execute learning.dbm.learn(next_target_arr,1,# If approximation is the Contrastive Divergence, this parameter is `k` in CD method.batch_size=200,# Batch size in mini-batch training.r_batch_size=-1# if `r_batch_size` > 0, the function of `dbm.learn` is a kind of reccursive learning.)If you want to know how to minimize the reconstructed error, see my Jupyter notebook:demo/demo_stacked_auto_encoder.ipynb.PerformanceRun a program:test/demo_stacked_auto_encoder.pytimepythontest/demo_stacked_auto_encoder.pyThe result is follow.real1m59.875s
user1m30.642s
sys0m29.232sDetailThis experiment was performed under the following conditions.Machine typevCPU:2memory:8GBCPU Platform: Intel Ivy BridgeObservation Data PointsThe observated data is the result ofnp.random.normal(loc=0.5, scale=0.2, size=(10000, 10000)).Number of unitsVisible layer:10000hidden layer(feature point):10hidden layer:10000Activation functionsvisible:                Logistic Functionhidden(feature point):  Logistic Functionhidden:                 Logistic FunctionApproximationContrastive DivergenceHyper parametersLearning rate:0.05Dropout rate:0.5Feature points[[0.092057   0.08856277 0.08699257 ... 0.09167331 0.08937846 0.0880063 ]
 [0.09090537 0.08669612 0.08995347 ... 0.08641837 0.08750935 0.08617442]
 [0.10187259 0.10633451 0.10060372 ... 0.10170306 0.10711189 0.10565192]
 ...
 [0.21540273 0.21737737 0.20949192 ... 0.20974982 0.2208562  0.20894371]
 [0.30749327 0.30964707 0.2850683  ... 0.29191507 0.29968456 0.29075691]
 [0.68022984 0.68454348 0.66431651 ... 0.67952715 0.6805653  0.66243178]]Reconstruct error[ 0.11668085 0.07513545 0.091044  ...,  0.0719339  0.07976882 0.09121697]Usecase: Building the RTRBM for recursive learning.Import Python and Cython modules.# Logistic Function as activation function.frompydbm.activation.logistic_functionimportLogisticFunction# Tanh Function as activation function.frompydbm.activation.tanh_functionimportTanhFunction# Stochastic Gradient Descent(SGD) as optimizer.frompydbm.optimization.optparams.sgdimportSGD# The `Client` in Builder Pattern for building RTRBM.frompydbm.dbm.recurrent_temporal_rbmimportRecurrentTemporalRBMInstantiate objects and execute learning.# The `Client` in Builder Pattern for building RTRBM.rt_rbm=RecurrentTemporalRBM(# The number of units in visible layer.visible_num=observed_arr.shape[-1],# The number of units in hidden layer.hidden_num=100,# The activation function in visible layer.visible_activating_function=TanhFunction(),# The activation function in hidden layer.hidden_activating_function=TanhFunction(),# The activation function in RNN layer.rnn_activating_function=LogisticFunction(),# is-a `OptParams`.opt_params=SGD(),# Learning rate.learning_rate=1e-05)Learning.Thert_rbmhas alearnmethod, to execute learning observed data points. This method can receive anp.ndarrayof observed data points, which is a rank-3 array-like or sparse matrix of shape: (The number of samples,The length of cycle,The number of features), as the first argument.# Learning.rt_rbm.learn(# The `np.ndarray` of observed data points.observed_arr,# Training count.training_count=1000,# Batch size.batch_size=200)Inferencing.After learning, thert_rbmprovides a function ofinferencemethod.# Execute recursive learning.inferenced_arr=rt_rbm.inference(test_arr,training_count=1,r_batch_size=-1)The shape oftest_arris equivalent toobserved_arr. Returned valueinferenced_arris generated by input parametertest_arrand can be considered as a feature expression oftest_arrbased on the distribution ofobserved_arr. In other words, the features ofinferenced_arris a summary of time series information intest_arrand then the shape is rank-2 array-like or sparse matrix: (The number of samples,The number of features).Feature points.On the other hand, thert_rbmhas arbmwhich also stores the feature points in hidden layers. To extract this embedded data, call the method as follows.feature_points_arr=rt_rbm.rbm.get_feature_points()The shape offeature_points_arris rank-2 array-like or sparse matrix: (The number of samples,The number of units in hidden layers). So this matrix also means time series data embedded as manifolds.Reconstructed data.Although RTRBM itself is not an Auto-Encoder, it can be described as a reconstruction model. In this library, this model has an input reconstruction function.reconstructed_arr=rt_rbm.rbm.get_reconstructed_arr()The shape ofreconstructed_arris equivalent toobserved_arr.If you want to know how to measure its reconstruction errors, see my Jupyter notebook:demo/demo_rt_rbm.ipynb.Save pre-learned parameters.The objectrt_rbm, which is-aRecurrentTemporalRBM, has the methodsave_pre_learned_params, to store the pre-learned parameters in a compressedNPY formatfile.rt_rbm.save_pre_learned_params("/var/tmp/demo_rtrbm.npz")Transfer learning in RTRBM.__init__method ofRecurrentTemporalRBMcan be givenpre_learned_path_listwhich is astrof file path that stores pre-learned parameters.# The `Client` in Builder Pattern for building RTRBM.rt_rbm=RecurrentTemporalRBM(# The number of units in visible layer.visible_num=observed_arr.shape[-1],# The number of units in hidden layer.hidden_num=100,# The activation function in visible layer.visible_activating_function=TanhFunction(),# The activation function in hidden layer.hidden_activating_function=TanhFunction(),# The activation function in RNN layer.rnn_activating_function=LogisticFunction(),# is-a `OptParams`.opt_params=SGD(),# Learning rate.learning_rate=1e-05,# File path that stores pre-learned parameters.pre_learned_path="/var/tmp/demo_rtrbm.npz")# Learning.rt_rbm.learn(# The `np.ndarray` of observed data points.observed_arr,# Training count.training_count=1000,# Batch size.batch_size=200)Usecase: Building the RNN-RBM for recursive learning.Import notRecurrentTemporalRBMbutRNNRBM, which is-aRecurrentTemporalRBM.# The `Client` in Builder Pattern for building RNN-RBM.frompydbm.dbm.recurrenttemporalrbm.rnn_rbmimportRNNRBMInstantiate objects.# The `Client` in Builder Pattern for building RNN-RBM.rt_rbm=RNNRBM(# The number of units in visible layer.visible_num=observed_arr.shape[-1],# The number of units in hidden layer.hidden_num=100,# The activation function in visible layer.visible_activating_function=TanhFunction(),# The activation function in hidden layer.hidden_activating_function=TanhFunction(),# The activation function in RNN layer.rnn_activating_function=LogisticFunction(),# is-a `OptParams`.opt_params=SGD(),# Learning rate.learning_rate=1e-05)The function of learning, inferencing, saving pre-learned parameters, and transfer learning are equivalent tort_rbmof RTRBM. SeeUsecase: Building the RTRBM for recursive learning..If you want to know how to measure its reconstruction errors, see my Jupyter notebook:demo/demo_rnn_rbm.ipynb.Usecase: Building the LSTM-RTRBM for recursive learning.Import notRecurrentTemporalRBMbutLSTMRTRBM, which is-aRecurrentTemporalRBM.# The `Client` in Builder Pattern for building LSTM-RTRBM.frompydbm.dbm.recurrenttemporalrbm.lstm_rt_rbmimportLSTMRTRBMInstantiate objects.# The `Client` in Builder Pattern for building RNN-RBM.rt_rbm=LSTMRTRBM(# The number of units in visible layer.visible_num=observed_arr.shape[-1],# The number of units in hidden layer.hidden_num=100,# The activation function in visible layer.visible_activating_function=TanhFunction(),# The activation function in hidden layer.hidden_activating_function=TanhFunction(),# The activation function in RNN layer.rnn_activating_function=LogisticFunction(),# is-a `OptParams`.opt_params=SGD(),# Learning rate.learning_rate=1e-05)The function of learning, inferencing, saving pre-learned parameters, and transfer learning are equivalent tort_rbmof RTRBM. SeeUsecase: Building the RTRBM for recursive learning..If you want to know how to measure its reconstruction errors, see my Jupyter notebook:demo/demo_lstm_rt_rbm.ipynb.Usecase: Image segmentation by Shape-BM.First, acquire image data and binarize it.fromPILimportImageimg=Image.open("horse099.jpg")imgIf you think the size of your image datasets may be large, resize it to an arbitrary size.img=img.resize((255,255))Convert RGB images to binary images.img_bin=img.convert("1")img_binSet up hyperparameters.filter_size=5overlap_n=4learning_rate=0.01filter_sizeis the 'filter' size. This value must be more than4. Andoverlap_nis hyperparameter specific to Shape-BM. In the visible layer, this model has so-called local receptive fields by connecting each first hidden unit only to a subset of the visible units, corresponding to one of four square patches. Each patch overlaps its neighbor byoverlap_npixels (Eslami, S. A., et al, 2014).Please notethat the recommended ratio offilter_sizeandoverlap_nis 5:4. It is not a constraint demanded by pure theory of Shape Boltzmann Machine itself but is a kind of limitation to simplify design and implementation in this library.And import Python and Cython modules.# The `Client` in Builder Patternfrompydbm.dbm.deepboltzmannmachine.shape_boltzmann_machineimportShapeBoltzmannMachine# The `Concrete Builder` in Builder Pattern.frompydbm.dbm.builders.dbm_multi_layer_builderimportDBMMultiLayerBuilderInstantiate objects and call the method.dbm=ShapeBoltzmannMachine(DBMMultiLayerBuilder(),learning_rate=learning_rate,overlap_n=overlap_n,filter_size=filter_size)img_arr=np.asarray(img_bin)img_arr=img_arr.astype(np.float64)# Execute learning.dbm.learn(# `np.ndarray` of image data.img_arr,# If approximation is the Contrastive Divergence, this parameter is `k` in CD method.training_count=1,# Batch size in mini-batch training.batch_size=300,# if `r_batch_size` > 0, the function of `dbm.learn` is a kind of reccursive learning.r_batch_size=-1,# Learning with the stochastic gradient descent(SGD) or not.sgd_flag=True)Extractdbm.visible_points_arras the observed data points in visible layer. Thisnp.ndarrayis segmented image data.inferenced_data_arr=dbm.visible_points_arr.copy()inferenced_data_arr=255-inferenced_data_arrImage.fromarray(np.uint8(inferenced_data_arr))Save pre-learned parameters and transfer learning in Shape Boltzmann Machine.In transfer learning problem setting,ShapeBoltzmannMachineis functionally equivalent toStackedAutoEncoder. SeeUsecase: Extracting all feature points for dimensions reduction(or pre-learning).Usecase: Casual use by facade for building Encoder/Decoder based on LSTM.Importfacademodule for building Encoder/Decoder based on LSTM.frompydbm.rnn.facade_encoder_decoderimportFacadeEncoderDecoderIf you want to use an Attention mechanism, importFacadeAttentionEncoderDecoderinstead.frompydbm.rnn.facade_attention_encoder_decoderimportFacadeAttentionEncoderDecoderasFacadeEncoderDecoderInstantiate object and call the method to learn observed data points.# `Facade` for casual user of Encoder/Decoder based on LSTM networks.facade_encoder_decoder=FacadeEncoderDecoder(# The number of units in input layers.input_neuron_count=observed_arr.shape[-1],# The length of sequences.# This means refereed maxinum step `t` in feedforward.seq_len=observed_arr.shape[1],# Refereed maxinum step `t` in BPTT. If `0`, this class referes all past data in BPTT.bptt_tau=observed_arr.shape[1],# Verbose mode or not. If `True`, this class sets the logger level as `DEBUG`.verbose_flag=True)Execute learning.facade_encoder_decoder.learn(observed_arr=observed_arr,target_arr=observed_arr)This method can receive anp.ndarrayof observed data points, which is a rank-3 array-like or sparse matrix of shape: (The number of samples,The length of cycle,The number of features), as the first and second argument. If the value of this second argument is not equivalent to the first argument and the shape is (The number of samples,The number of features), in other words, the rank is 2, the function ofencoder_decoder_controllercorresponds to a kind of Regression model.After learning, thefacade_encoder_decoderprovides a function ofinferencemethod.# Execute recursive learning.inferenced_arr=facade_encoder_decoder.inference(test_arr)The shape oftest_arrandinferenced_arrare equivalent toobserved_arr. Returned valueinferenced_arris generated by input parametertest_arrand can be considered as a decoded data points based on encodedtest_arr.On the other hand, thefacade_encoder_decoderalso stores the feature points in hidden layers. To extract this embedded data, call the method as follows.feature_points_arr=facade_encoder_decoder.get_feature_points()The shape offeature_points_arris rank-2 array-like or sparse matrix: (The number of samples,The number of units in hidden layers). So this matrix also means time series data embedded as manifolds.You can check the reconstruction error rate. Callget_reconstruct_errormethod as follow.reconstruct_error_arr=facade_encoder_decoder.get_reconstruction_error()If you want to know how to minimize the reconstructed error, see my Jupyter notebook:demo/demo_sine_wave_prediction_by_LSTM_encoder_decoder.ipynb.Save pre-learned parameters.The objectfacade_encoder_decoderhas the methodsave_pre_learned_params, to store the pre-learned parameters in compressedNPY formatfiles.facade_encoder_decoder.save_pre_learned_params(# File path that stores Encoder's parameters.encoder_file_path="/var/tmp/encoder.npz",# File path that stores Decoder's parameters.decoder_file_path="/var/tmp/decoder.npz")Transfer learning in Encoder/Decoder based on LSTM.__init__method ofFacadeEncoderDecodercan be givenencoder_pre_learned_file_pathanddecoder_pre_learned_file_path, which arestrof file path that stores Encoder/Decoder's pre-learned parameters.facade_encoder_decoder2=FacadeEncoderDecoder(# The number of units in input layers.input_neuron_count=observed_arr.shape[-1],# The length of sequences.# This means refereed maxinum step `t` in feedforward.seq_len=observed_arr.shape[1],# Refereed maxinum step `t` in BPTT. If `0`, this class referes all past data in BPTT.bptt_tau=observed_arr.shape[1],# File path that stored Encoder's pre-learned parameters.encoder_pre_learned_file_path="/var/tmp/encoder.npz",# File path that stored Decoder's pre-learned parameters.decoder_pre_learned_file_path="/var/tmp/decoder.npz",# Verbose mode or not. If `True`, this class sets the logger level as `DEBUG`.verbose_flag=True)facade_encoder_decoder2.learn(observed_arr=observed_arr,target_arr=observed_arr)For more detail settings.__init__ofFacadeEncoderDecodercan be given many parameters as follows.# `Facade` for casual user of Encoder/Decoder based on LSTM networks.facade_encoder_decoder=FacadeEncoderDecoder(# The number of units in input layers.input_neuron_count=observed_arr.shape[-1],# The number of units in hidden layers.hidden_neuron_count=200,# Epochs of Mini-batch.epochs=200,# Batch size of Mini-batch.batch_size=20,# Learning rate.learning_rate=1e-05,# Attenuate the `learning_rate` by a factor of this value every `attenuate_epoch`.learning_attenuate_rate=0.1,# Attenuate the `learning_rate` by a factor of `learning_attenuate_rate` every `attenuate_epoch`.attenuate_epoch=50,# Activation function in hidden layers.hidden_activating_function=LogisticFunction(),# Activation function in output layers.output_activating_function=LogisticFunction(),# Loss function.computable_loss=MeanSquaredError(),# Optimizer which is-a `OptParams`.opt_params=Adam(),# The length of sequences.# This means refereed maxinum step `t` in feedforward.seq_len=8,# Refereed maxinum step `t` in Backpropagation Through Time(BPTT).# If `0`, this class referes all past data in BPTT.bptt_tau=8,# Size of Test data set. If this value is `0`, the validation will not be executed.test_size_rate=0.3,# Tolerance for the optimization.# When the loss or score is not improving by at least tol# for two consecutive iterations, convergence is considered# to be reached and training stops.tol=0.0,# Tolerance for deviation of loss.tld=1.0,# Verification function.verificatable_result=VerificateFunctionApproximation(),# Verbose mode or not. If `True`, this class sets the logger level as `DEBUG`.verbose_flag=True)If you want to not only use casually the model but also hack it, seeUsecase: Build Encoder/Decoder based on LSTM as a reconstruction model..Usecase: Build Encoder/Decoder based on LSTM or ConvLSTM as a reconstruction model.Consider functionally reusability and possibility of flexible design, you should use notFacadeEncoderDecoderbutEncoderDecoderControlleras follows.Setup logger for verbose output.fromloggingimportgetLogger,StreamHandler,NullHandler,DEBUG,ERRORlogger=getLogger("pydbm")handler=StreamHandler()handler.setLevel(DEBUG)logger.setLevel(DEBUG)logger.addHandler(handler)Import Python and Cython modules for computation graphs.# LSTM Graph which is-a `Synapse`.frompydbm.synapse.recurrenttemporalgraph.lstm_graphimportLSTMGraphasEncoderGraphfrompydbm.synapse.recurrenttemporalgraph.lstm_graphimportLSTMGraphasDecoderGraphIf you want to introduce the graph of decoder for building an Attention mechanism as the decoder, importAttentionLSTMGraphinstead.frompydbm.synapse.recurrenttemporalgraph.lstmgraph.attention_lstm_graphimportAttentionLSTMGraphasDecoderGraphImport Python and Cython modules of activation functions.# Logistic Function as activation function.frompydbm.activation.logistic_functionimportLogisticFunction# Tanh Function as activation function.frompydbm.activation.tanh_functionimportTanhFunctionImport Python and Cython modules for loss function.# Loss function.frompydbm.loss.mean_squared_errorimportMeanSquaredErrorImport Python and Cython modules for optimizer.# SGD as a optimizer.frompydbm.optimization.optparams.sgdimportSGDasEncoderSGDfrompydbm.optimization.optparams.sgdimportSGDasDecoderSGDIf you want to use not Stochastic Gradient Descent(SGD) butAdamoptimizer, importAdam.# Adam as a optimizer.frompydbm.optimization.optparams.adamimportAdamasEncoderAdamfrompydbm.optimization.optparams.adamimportAdamasDecoderAdamFuthermore, import class for verification of function approximation.# Verification.frompydbm.verification.verificate_function_approximationimportVerificateFunctionApproximationThe activation by softmax function can be verificated byVerificateSoftmax.frompydbm.verification.verificate_softmaximportVerificateSoftmaxAnd import LSTM Model and Encoder/Decoder schema.# LSTM model.frompydbm.rnn.lstm_modelimportLSTMModelasEncoderfrompydbm.rnn.lstm_modelimportLSTMModelasDecoder# Encoder/Decoderfrompydbm.rnn.encoder_decoder_controllerimportEncoderDecoderControllerIf you want to build an Attention mechanism as the decoder, importAttentionLSTMModelinstead.frompydbm.rnn.lstmmodel.attention_lstm_modelimportAttentionLSTMModelasDecoderInstantiateEncoder.# Init.encoder_graph=EncoderGraph()# Activation function in LSTM.encoder_graph.observed_activating_function=TanhFunction()encoder_graph.input_gate_activating_function=LogisticFunction()encoder_graph.forget_gate_activating_function=LogisticFunction()encoder_graph.output_gate_activating_function=LogisticFunction()encoder_graph.hidden_activating_function=TanhFunction()encoder_graph.output_activating_function=LogisticFunction()# Initialization strategy.# This method initialize each weight matrices and biases in Gaussian distribution: `np.random.normal(size=hoge) * 0.01`.encoder_graph.create_rnn_cells(input_neuron_count=observed_arr.shape[-1],hidden_neuron_count=200,output_neuron_count=1)# Optimizer for Encoder.encoder_opt_params=EncoderAdam()encoder_opt_params.weight_limit=1e+03encoder_opt_params.dropout_rate=0.5encoder=Encoder(# Delegate `graph` to `LSTMModel`.graph=encoder_graph,# Refereed maxinum step `t` in BPTT. If `0`, this class referes all past data in BPTT.bptt_tau=8,# Size of Test data set. If this value is `0`, the validation will not be executed.test_size_rate=0.3,# Loss function.computable_loss=MeanSquaredError(),# Optimizer.opt_params=encoder_opt_params,# Verification function.verificatable_result=VerificateFunctionApproximation(),# Tolerance for the optimization.# When the loss or score is not improving by at least tol# for two consecutive iterations, convergence is considered# to be reached and training stops.tol=0.0)InstantiateDecoder.# Init.decoder_graph=DecoderGraph()# Activation function in LSTM.decoder_graph.observed_activating_function=TanhFunction()decoder_graph.input_gate_activating_function=LogisticFunction()decoder_graph.forget_gate_activating_function=LogisticFunction()decoder_graph.output_gate_activating_function=LogisticFunction()decoder_graph.hidden_activating_function=TanhFunction()decoder_graph.output_activating_function=LogisticFunction()# Initialization strategy.# This method initialize each weight matrices and biases in Gaussian distribution: `np.random.normal(size=hoge) * 0.01`.decoder_graph.create_rnn_cells(input_neuron_count=200,hidden_neuron_count=200,output_neuron_count=observed_arr.shape[-1])# Optimizer for Decoder.decoder_opt_params=DecoderAdam()decoder_opt_params.weight_limit=1e+03decoder_opt_params.dropout_rate=0.5decoder=Decoder(# Delegate `graph` to `LSTMModel`.graph=decoder_graph,# The length of sequences.seq_len=8,# Refereed maxinum step `t` in BPTT. If `0`, this class referes all past data in BPTT.bptt_tau=8,# Loss function.computable_loss=MeanSquaredError(),# Optimizer.opt_params=decoder_opt_params,# Verification function.verificatable_result=VerificateFunctionApproximation(),# Tolerance for the optimization.# When the loss or score is not improving by at least tol# for two consecutive iterations, convergence is considered# to be reached and training stops.tol=0.0)InstantiateEncoderDecoderControllerand delegateencoderanddecoderto this object.encoder_decoder_controller=EncoderDecoderController(# is-a LSTM model.encoder=encoder,# is-a LSTM model.decoder=decoder,# The number of epochs in mini-batch training.epochs=200,# The batch size.batch_size=100,# Learning rate.learning_rate=1e-05,# Attenuate the `learning_rate` by a factor of this value every `attenuate_epoch`.learning_attenuate_rate=0.1,# Attenuate the `learning_rate` by a factor of `learning_attenuate_rate` every `attenuate_epoch`.attenuate_epoch=50,# Size of Test data set. If this value is `0`, the validation will not be executed.test_size_rate=0.3,# Loss function.computable_loss=MeanSquaredError(),# Verification function.verificatable_result=VerificateFunctionApproximation(),# Tolerance for the optimization.# When the loss or score is not improving by at least tol# for two consecutive iterations, convergence is considered# to be reached and training stops.tol=0.0)If you want to use ConvLSTM asencoderanddecoder, instantiateConvLSTMModelwhich is-aLSTMModeland is-aReconstructableModel. See my jupyter notebook for details:demo/demo_conv_lstm.ipynb.In any case, let's execute learning after instantiation is complete.# Learning.encoder_decoder_controller.learn(observed_arr,observed_arr)If you delegatedLSTMModels asencoderanddecoder, this method can receive anp.ndarrayof observed data points, which is arank-3 array-like or sparse matrixof shape: (The number of samples,The length of cycle,The number of features), as the first and second argument. If the value of this second argument is not equivalent to the first argument and the shape is (The number of samples,The number of features), in other words, the rank is2, the function ofencoder_decoder_controllercorresponds to a kind of Regression model.On the other hand, if you delegatedConvLSTMModels asencoderanddecoder, the rank of matrix is5. The shape is:(The number of samples,The length of cycle,Channel,Height of images,Width of images).After learning, theencoder_decoder_controllerprovides a function ofinferencemethod.# Execute recursive learning.inferenced_arr=encoder_decoder_controller.inference(test_arr)The shape oftest_arrandinferenced_arrare equivalent toobserved_arr. Returned valueinferenced_arris generated by input parametertest_arrand can be considered as a decoded data points based on encodedtest_arr.On the other hand, theencoder_decoder_controlleralso stores the feature points in hidden layers. To extract this embedded data, call the method as follows.feature_points_arr=encoder_decoder_controller.get_feature_points()IfLSTMModels are delegated, the shape offeature_points_arrisrank-3 array-like or sparse matrix: (The number of samples,The length of cycle,The number of units in hidden layers). On the other hand, ifConvLSTMModels are delegated, the shape offeature_points_arrisrank-5 array-like or sparse matrix:(The number of samples,The length of cycle,Channel,Height of images,Width of images). So the matrices also mean time series data embedded as manifolds in the hidden layers.You can check the reconstruction error rate. Callget_reconstruct_errormethod as follow.reconstruct_error_arr=encoder_decoder_controller.get_reconstruction_error()If you want to know how to minimize the reconstructed error, see my Jupyter notebook:demo/demo_sine_wave_prediction_by_LSTM_encoder_decoder.ipynb.Usecase: Build Convolutional Auto-Encoder.Setup logger for verbose output and import Python and Cython modules in the same manner asUsecase: Build Encoder/Decoder based on LSTM as a reconstruction model.fromloggingimportgetLogger,StreamHandler,NullHandler,DEBUG,ERRORlogger=getLogger("pydbm")handler=StreamHandler()handler.setLevel(DEBUG)logger.setLevel(DEBUG)logger.addHandler(handler)# ReLu Function as activation function.frompydbm.activation.relu_functionimportReLuFunction# Tanh Function as activation function.frompydbm.activation.tanh_functionimportTanhFunction# Logistic Function as activation function.frompydbm.activation.logistic_functionimportLogisticFunction# Loss function.frompydbm.loss.mean_squared_errorimportMeanSquaredError# Adam as a optimizer.frompydbm.optimization.optparams.adamimportAdam# Verification.frompydbm.verification.verificate_function_approximationimportVerificateFunctionApproximationAnd import Python and Cython modules of the Convolutional Auto-Encoder.# Controller of Convolutional Auto-Encoderfrompydbm.cnn.convolutionalneuralnetwork.convolutional_auto_encoderimportConvolutionalAutoEncoder# First convolution layer.frompydbm.cnn.layerablecnn.convolution_layerimportConvolutionLayerasConvolutionLayer1# Second convolution layer.frompydbm.cnn.layerablecnn.convolution_layerimportConvolutionLayerasConvolutionLayer2# Computation graph for first convolution layer.frompydbm.synapse.cnn_graphimportCNNGraphasConvGraph1# Computation graph for second convolution layer.frompydbm.synapse.cnn_graphimportCNNGraphasConvGraph2InstantiateConvolutionLayers, delegatingCNNGraphs respectively.# First convolution layer.conv1=ConvolutionLayer1(# Computation graph for first convolution layer.ConvGraph1(# Logistic function as activation function.activation_function=LogisticFunction(),# The number of `filter`.filter_num=20,# Channel.channel=1,# The size of kernel.kernel_size=3,# The filter scale.scale=0.1,# The nubmer of stride.stride=1,# The number of zero-padding.pad=1))# Second convolution layer.conv2=ConvolutionLayer2(# Computation graph for second convolution layer.ConvGraph2(# Computation graph for second convolution layer.activation_function=LogisticFunction(),# The number of `filter`.filter_num=20,# Channel.channel=20,# The size of kernel.kernel_size=3,# The filter scale.scale=0.1,# The nubmer of stride.stride=1,# The number of zero-padding.pad=1))InstantiateConvolutionalAutoEncoderand setup parameters.cnn=ConvolutionalAutoEncoder(# The `list` of `ConvolutionLayer`.layerable_cnn_list=[conv1,conv2],# The number of epochs in mini-batch training.epochs=200,# The batch size.batch_size=100,# Learning rate.learning_rate=1e-05,# Attenuate the `learning_rate` by a factor of this value every `attenuate_epoch`.learning_attenuate_rate=0.1,# Attenuate the `learning_rate` by a factor of `learning_attenuate_rate` every `attenuate_epoch`.attenuate_epoch=50,# Size of Test data set. If this value is `0`, the validation will not be executed.test_size_rate=0.3,# Optimizer.opt_params=Adam(),# Verification.verificatable_result=VerificateFunctionApproximation(),# The rate of dataset for test.test_size_rate=0.3,# Tolerance for the optimization.# When the loss or score is not improving by at least tol# for two consecutive iterations, convergence is considered# to be reached and training stops.tol=1e-15)Execute learning.cnn.learn(img_arr,img_arr)img_arris anp.ndarrayof image data, which is a rank-4 array-like or sparse matrix of shape: (The number of samples,Channel,Height of image,Width of image), as the first and second argument. If the value of this second argument is not equivalent to the first argument and the shape is (The number of samples,The number of features), in other words, the rank is 2, the function ofcnncorresponds to a kind of Regression model.After learning, thecnnprovides a function ofinferencemethod.result_arr=cnn.inference(test_img_arr[:100])The shape oftest_img_arrandresult_arris equivalent toimg_arr.If you want to know how to visualize the reconstructed images, see my Jupyter notebook:demo/demo_convolutional_auto_encoder.ipynb.Save pre-learned parameters.The objectcnn, which is-aConvolutionalNeuralNetwork, has the methodsave_pre_learned_params, to store the pre-learned parameters in compressedNPY formatfiles.# Save pre-learned parameters.cnn.save_pre_learned_params(# Path of dir. If `None`, the file is saved in the current directory.dir_path="/var/tmp/",# The naming rule of files. If `None`, this value is `cnn`.file_name="demo_cnn")Transfer learning in Convolutional Auto-Encoder.__init__ofConvolutionalAutoEncoder, which is-aConvolutionalNeuralNetwork, can be givenpre_learned_path_listwhich is alistof file paths that store pre-learned parameters.cnn2=ConvolutionalAutoEncoder(layerable_cnn_list=[conv1,conv2],epochs=100,batch_size=batch_size,learning_rate=1e-05,learning_attenuate_rate=0.1,attenuate_epoch=25,computable_loss=MeanSquaredError(),opt_params=Adam(),verificatable_result=VerificateFunctionApproximation(),test_size_rate=0.3,tol=1e-15,save_flag=True,pre_learned_path_list=["pre-learned/demo_cnn_0.npz","pre-learned/demo_cnn_1.npz"])# Execute learning.cnn2.learn(img_arr,img_arr)Usecase: Build Spatio-Temporal Auto-Encoder.Setup logger for verbose output and import Python and Cython modules in the same manner asUsecase: Build Encoder/Decoder based on LSTM as a reconstruction model.Import Python and Cython modules of the Spatio-Temporal Auto-Encoder.frompydbm.cnn.spatio_temporal_auto_encoderimportSpatioTemporalAutoEncoderBuild Convolutional Auto-Encoder in the same manner asUsecase: Build Convolutional Auto-Encoder.and build Encoder/Decoder in the same manner asUsecase: Build Encoder/Decoder based on LSTM as a reconstruction model.InstantiateSpatioTemporalAutoEncoderand setup parameters.cnn=SpatioTemporalAutoEncoder(# The `list` of `LayerableCNN`.layerable_cnn_list=[conv1,conv2],# is-a `ReconstructableModel`.encoder=encoder,# is-a `ReconstructableModel`.decoder=decoder,# Epochs of Mini-batch.epochs=100,# Batch size of Mini-batch.batch_size=20,# Learning rate.learning_rate=1e-05,# Attenuate the `learning_rate` by a factor of this value every `attenuate_epoch`.learning_attenuate_rate=0.1,# Attenuate the `learning_rate` by a factor of `learning_attenuate_rate` every `attenuate_epoch`.attenuate_epoch=25,# Loss function.computable_loss=MeanSquaredError(),# Optimization function.opt_params=Adam(),# Verification function.verificatable_result=VerificateFunctionApproximation(),# Size of Test data set. If this value is `0`, the validation will not be executed.test_size_rate=0.3,# Tolerance for the optimization.tol=1e-15)Execute learning.cnn.learn(img_arr,img_arr)img_arris anp.ndarrayof image data, which is arank-5array-like or sparse matrix of shape: (The number of samples,The length of one sequence,Channel,Height of image,Width of image), as the first and second argument.After learning, thecnnprovides a function ofinferencemethod.result_arr=cnn.inference(test_img_arr[:100])If you want to know how to visualize the reconstructed video images, see my Jupyter notebook:demo/demo_spatio_temporal_auto_encoder.ipynb.Save pre-learned parameters.The objectcnn, which is-aSpatioTemporalAutoEncoder, has the methodsave_pre_learned_params, to store the pre-learned parameters in compressedNPY formatfiles.cnn.save_pre_learned_params("/var/tmp/spae/")Naming rule of saved files.spatio_cnn_X.npz: Pre-learned parameters inXlayer of Convolutional Auto-Encoder.temporal_encoder.npz: Pre-learned parameters in the Temporal Encoder.temporal_decoder.npz: Pre-learned parameters in the Temporal Decoder.Transfer learning in Spatio-Temporal Auto-Encoder.__init__method ofSpatioTemporalAutoEncodercan be givenpre_learned_dir, which is-astrof directory path that stores pre-learned parameters of the Convolutional Auto-Encoder and the Encoder/Decoder based on LSTM.cnn2=SpatioTemporalAutoEncoder(# The `list` of `LayerableCNN`.layerable_cnn_list=[conv1,conv2],# is-a `ReconstructableModel`.encoder=encoder,# is-a `ReconstructableModel`.decoder=decoder,# Epochs of Mini-batch.epochs=100,# Batch size of Mini-batch.batch_size=20,# Learning rate.learning_rate=1e-05,# Attenuate the `learning_rate` by a factor of this value every `attenuate_epoch`.learning_attenuate_rate=0.1,# Attenuate the `learning_rate` by a factor of `learning_attenuate_rate` every `attenuate_epoch`.attenuate_epoch=25,# Loss function.computable_loss=MeanSquaredError(),# Optimization function.opt_params=Adam(),# Verification function.verificatable_result=VerificateFunctionApproximation(),# Size of Test data set. If this value is `0`, the validation will not be executed.test_size_rate=0.3,# Tolerance for the optimization.tol=1e-15,# Path to directory that stores pre-learned parameters.pre_learned_dir="/var/tmp/spae/")cnn2.learn(img_arr,img_arr)Usecase: Build Optimizer.If you want to use various optimizers other than Stochastic Gradient Descent(SGD), instantiate each class as follows.Adaptive subgradient methods(AdaGrad).If you want to use Adaptive subgradient methods(AdaGrad) optimizer, importAdaGradand instantiate it.# AdaGrad as a optimizer.frompydbm.optimization.optparams.ada_gradimportAdaGrad# is-a `OptParams`.opt_params=AdaGrad()Adaptive RootMean-Square (RMSProp) gradient decent algorithm.If you want to use an optimizer of the Adaptive RootMean-Square (RMSProp) gradient decent algorithm, importRMSPropand instantiate it.# RMSProp as a optimizer.frompydbm.optimization.optparams.rms_propimportRMSProp# is-a `OptParams`.opt_params=RMSProp(# Decay rate.decay_rate=0.99)Nesterov's Accelerated Gradient(NAG).If you want to use the Nesterov's Accelerated Gradient(NAG) optimizer, importNAGand instantiate it.# Adam as a optimizer.frompydbm.optimization.optparams.nagimportNAG# is-a `OptParams`.opt_params=NAG(# Momentum.momentum=0.9)Adaptive Moment Estimation(Adam).If you want to use the Adaptive Moment Estimation(Adam) optimizer, importAdamand instantiate it.# Adam as a optimizer.frompydbm.optimization.optparams.adamimportAdam# is-a `OptParams`.opt_params=Adam(# BETA 1.beta_1=0.9,# BETA 2.beta_2=0.99,# Compute bias-corrected first moment / second raw moment estimate or not.bias_corrected_flag=False)Nesterov-accelerated Adaptive Moment Estimation(Nadam).If you want to use the Nesterov-accelerated Adaptive Moment Estimation(Nadam) optimizer, importNadamand instantiate it.# Nadam as a optimizer.frompydbm.optimization.optparams.nadamimportNadam# is-a `OptParams`.opt_params=Nadam(# BETA 1.beta_1=0.9,# BETA 2.beta_2=0.99,# Compute bias-corrected first moment / second raw moment estimate or not.bias_corrected_flag=False)Usecase: Tied-weights.An Auto-Encoder is guaranteed to have a well-defined energy function if it has tied weights. It reduces the number of parameters."It is interesting to note that for an autoencoder whose weights are not tied, contractive regularization will encourage the vector field to be conservative. The reason is that encouraging the first derivative to be small and the second derivative to be negative will tend to bound the energy surface near the training."Kamyshanska, H., & Memisevic, R. (2014). The potential energy of an autoencoder. IEEE transactions on pattern analysis and machine intelligence, 37(6), 1261-1273., p7.In this library,ConvolutionalAutoEncoder's weights are tied in default. But the weight matrixs ofSimpleAutoEncoderwhich has twoNeuralNetworks are not tied. If you want to tie the weights, set thetied_graphas follows.frompydbm.synapse.nn_graphimportNNGraphfrompydbm.activation.identity_functionimportIdentityFunction# Encoder's graph.encoder_graph=NNGraph(activation_function=IdentityFunction(),hidden_neuron_count=100,output_neuron_count=10,)# Decoder's graph.decoder_graph=NNGraph(activation_function=IdentityFunction(),hidden_neuron_count=10,output_neuron_count=100,)# Set encoder's graph.decoder_graph.tied_graph=encoder_graphUsecase: Build and delegate image generator.ConvolutionalAutoEncoderandSpatioTemporalAutoEncoder, which areConvolutionalNeuralNetworks, provide a methodlearn_generatedwhich can be delegated anImageGenerator.ImageGeneratoris an Iterates to reads batches of images from local directories for mini-batch training.# Image generator for Auto-Encoder or Encoder/Decoder scheme.frompydbm.cnn.featuregenerator.image_generatorimportImageGeneratorfeature_generator=ImageGenerator(# Epochs of Mini-batch.epochs=100,# Batch size of Mini-batch.batch_size=20,# Path of directory which stores image files for training.training_image_dir="img/training/",# Path of directory which stores image files for test.test_image_dir="img/test/",# The length of one sequence.# If `None`, generated `np.ndarray` of images will be rank-4 matrices.seq_len=10,# Gray scale or not.gray_scale_flag=True,# Height and width of images. The shape is: Tuple(`width`, `height`).wh_size_tuple=(94,96),# Normalization mode. `z_score` or `min_max`.norm_mode="z_score")Delegatefeature_generatortocnn.cnn.learn_generated(feature_generator)Methodlearn_generatedis functionally equivalent to methodlearn.Usecase: Save and load the pre-learned parameters in computation graphs.For file management of pre-learned parameters in the transfer learning problem setting, each computation graph, which is-aSynapse, provides two methods:save_pre_learned_paramsandload_pre_learned_params.# Save pre-learned parameters.synapse.save_pre_learned_params("/var/tmp/pre_learned.npz")The function of this method is to store the pre-learned parameters in compressedNPY formatfiles.And call the methodload_pre_learned_paramsto execute transfer learning or re-learn.# Load pre-learned parameters.synapse.load_pre_learned_params("/var/tmp/pre_learned.npz")The classSynapsehas sub-classes:CompleteBipartiteGraph,LSTMGraph,CNNGraph, and so on. 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Recurrent neural network regularization. arXiv preprint arXiv:1409.2329.Related PoC量子力学、統計力学、熱力学における天才物理学者たちの神学的な形象について(Japanese)熱力学の前史、マクスウェル＝ボルツマン分布におけるエントロピーの歴史的意味論メディアとしての統計力学と形式としてのアンサンブル、そのギブス的類推「マクスウェルの悪魔」、力学の基礎法則としての神Webクローラ型人工知能によるパラドックス探索暴露機能の社会進化論(Japanese)World-Wide Webの社会構造とWebクローラ型人工知能の意味論意味論の意味論、観察の観察深層強化学習のベイズ主義的な情報探索に駆動された自然言語処理の意味論(Japanese)平均場近似推論の統計力学、自己符号化器としての深層ボルツマンマシン深層学習の計算コスト削減、MobileNetの設計思想ニューラルネットワーク最適化問題におけるアルゴリズム設計の物理学的な意味論正則化問題における敵対的生成ネットワーク(GANs)と敵対的自己符号化器(AAEs)のネットワーク構造階層的潜在変数モデルをメディアとしたラダーネットワークの半教師あり学習形式、ノイズ除去型自己符号化器の機能エネルギーベースモデルとしての敵対的生成ネットワーク(GAN)と自己符号化器におけるリアプノフ安定ニューラルネットワーク言語モデルの自然言語処理と再帰的ニューラルネットワークのネットワーク構造転移学習のパラドックス、脱パラドックス化の形式としての半教師あり学習ハッカー倫理に準拠した人工知能のアーキテクチャ設計(Japanese)アーキテクチャ中心設計の社会構造とアーキテクチャの意味論近代社会の社会構造とハッカー倫理の意味論ラショナル統一プロセス(RUP)の社会構造とアーキテクチャ設計の意味論オブジェクト指向のオブジェクト指向「人工の理想」を背景とした「万物照応」のデータモデリング(Japanese)探偵の機能的等価物としての異常検知モデル、謎解きの推論アルゴリズムMore detail demosWebクローラ型人工知能：キメラ・ネットワークの仕様(Japanese)Implemented by theC++version of this library, these 20001 bots are able to execute the dimensions reduction(or pre-learning) for natural language processing to run as 20001 web-crawlers and 20001 web-scrapers.ロボアドバイザー型人工知能：キメラ・ネットワークの仕様(Japanese)The 20001 bots can also simulate the portfolio optimization of securities such as stocks and circulation currency such as cryptocurrencies.Authorchimera0(RUM)Author URIhttp://accel-brain.com/LicenseGNU General Public License v2.0