Jan-Willem van de Meent, Brooks Paige, Hongseok Yang, Frank Wood. Limits of Naive Bayesian The limits naturally comes from two parts, estimation of and. For example, you might predict the annual income of a person based on. The improvement is a big milestone for PyTorch and includes new developer tools, new APIs, TensorBoard support and much more. The network itself was built with Keras, like all the other networks our team has built from scratch so far, although we have adapted some third party networks written in Caffe and. Back propagation from scratch Papers discussed. Building neural networks wasn't just easy, it was fun. The wonderful software PennyLane by Xanadu evaluates such derivatives using a simple formula which gives an exact answer, albeit only in special cases. Recent results at the intersection of Bayesian modelling and deep learning offer a Bayesian interpretation of. The lectures cover artificial neural networks (deep learning), reinforcement learning, Bayesian modeling, model comparison and fitting, classification, probabilistic graphical models, and program induction. With PyTorch, you can dynamically build neural networks and easily perform advanced Artificial Intelligence tasks. In Neural Networks and deep neural networks what does label-dropout mean If you take the following sentence from an article on deep neural networks to regularize the classifier layer by estimating the marginalized effect of label-dropout during training. Neural Networks TensorFlow CNTK Natural Language Processing Cognitive Computing GeoAI Computer Vision Dimensionality Reduction Object Detection Support Vector Machines Object Tracking Keras PyTorch scikit-learn fast. Notebooks - A starter kit for Jupyter notebooks and machine learning. Finding the right architecture and hyperparameter settings for training a deep neural network is crucial to achieve top performance. pdf understanding convolutional neural networks through visualizations in pytorch. 1) Plain Tanh Recurrent Nerual Networks. Apply now for jobs that are hiring near you. Then when doing a one-shot classification task described above, the network can compare the test image to each image in the support set,. He has also worked on a broad range of applications of machine learning in domains ranging from computer vision to healthcare.
The output from the Enter Data module is combined with the output from the Train Model module. They can be used to boil a sequence down into a high-level understanding, to annotate sequences, and even to generate new sequences from scratch!. Modeling such times series with onlyVAR or only RNNs can lead. George Dahl, et al. Usually, when training a neural network, we try to find the parameter θ* which minimizes L n (θ). neural networks and deep learning frameworks robot learning & industrial applications biologically inspired models unsupervised learning: PCA, ICA, SVD, GANs lecturing undergraduate (AI) and graduate (machine learning) programs supervision of Master students & mentoring of Ph. Implement deep learning models in Python using the PyTorch library and train them with real-world. Pytorch is a dynamic instead of static deep learning library and Jeremy Writes that nearly all of the top 10 Kaggle competition winners now have been using Pytorch. Graves, Alex, Greg Wayne, Malcolm Reynolds, Tim Harley, Ivo Danihelka, Agnieszka Grabska-Barwińska, Sergio Gómez Colmenarejo et al. Neural networks to communicate with Alexa devices using sign language Twitter bot purge Rush Hour puzzle solver and generator Changing Twitter, with Statistics Street network orientation in major cities Expect the unexpected: Telling stories with open data Products with tariffs in the trade war Doing good data science. Package for causal inference in graphs and in the pairwise settings for Python>=3. ai course the focus was to allow student so read and implement recent research papers, and pytorch made this easier due to its flexibility. The rest of this paper is organized as follows. Diet: Forget government-issued food pyramids. In the quantum neural net field, in order to do backpropagation, one often wishes to take the derivative of a unitary matrix with respect to a parameter it depends on. The implementation follows Yarin Gal's papers "Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning" (see BDropout) and "Concrete Dropout" (see CDropout).
pdf bayesian neural network series post 1_ need for bayesian networks. 5 Tensor Flow. Dilated Residual Networks pytorch-semantic-segmentation PyTorch for Semantic Segmentation keras-visualize-activations Activation Maps Visualisation for Keras. Here are simple steps to improve your experience with Colab. Equi-normalization of Neural Networks. The output from the Enter Data module is combined with the output from the Train Model module. This work enables practical deep learning while preserving benefits of Bayesian principles. May 01, 2019 · PyTorch 1. This involves working in physics-based simulations and on actual robot hardware. A Bayesian seismic monitoring system, NET-VISA, has been built comprising a spatial event prior and generative models of event transmission and detection, as well as an inference algorithm. A network of deep neural networks for distant speech recognition. The problem that both Convolutional Neural Networks and Recurrent Neural Networks solve is constructing an efficient neural network for the case where the size of the input is large or unrestricted. The probability of the binary vector can then be obtained by taking the product of these conditionals. The main idea is to train a variational auto-encoder (VAE) on the MNIST dataset and run Bayesian Optimization in the latent space. Writing your first Bayesian Neural Network in Pyro and PyTorch. 2 Requirements Good knowledge of Pytorch or Tensor ow and especially Python. Bayesian Optimization in PyTorch. at NPS 2018, where they devised a very simple and practical method for uncertainty using bootstrap and randomized priors and decided to share the PyTorch code.
But, even then, the talk of automating human tasks with machines looks a bit far fetched. Feedforward neural nets model p(y|x, θ) as a nonlinear function of θ and x. The talk will include. You will implement this model for Assignment 4. , how fast can a neural network achieve a pre-defined accuracy (e. High degree of self-motivation. Notebooks - A starter kit for Jupyter notebooks and machine learning. Hinton's delivery is humorous. A PyTorch implementation will be available as a plug-and-play optimiser. For example, a Bayesian network could represent the probabilistic relationships between diseases and symptoms. If you have studied the concept of regularization in machine learning, you will have a fair idea that regularization penalizes the coefficients. Luxembourg - Design of machine learning methods for fraud detection (non-technical losses) in energy distribution networks in a colaboration between private company and university: using recurrent neural networks, covariate-shift adaptation methods, and. Until the advent of DyNet at CMU, and PyTorch at Facebook, Chainer was the leading neural network framework for. Recurrent neural networks are one of the staples of deep learning, allowing neural networks to work with sequences of data like text, audio and video. In this course, you will learn how neural networks can be applied to text data. arxiv pytorch:star: A network of deep neural networks for distant speech recognition. Understand PyTorch and Deep Learning concepts; Build your neural network using Deep Learning techniques in PyTorch.
In conclusion you will get acquainted with natural language processing and text processing using PyTorch. Hyperparameters Optimization in Deep Convolutional Neural Network / Bayesian Approach with Gaussian Process Prior. Generative adversarial networks Building a deep generative model of MNIST digits. Is there any algorithm that would help in this situation? Also, would some other supervised learning algorithm fit better here than a neural network?. Echo state networks (ESN) provide an architecture and supervised learning principle for recurrent neural networks (RNNs). The second day focuses on a popular machine learning approach 'Deep-learning' which mimics the deep neural network structure in our brain, in order to predict complex phenomena of nature. In a Bayesian neural network, the mapping from the input to the last. parameters so that we can optimise. Source: CycleGAN. Networks Bayesian Neural Networks 297of 806 Neural Networks 2: Overview Recall: we would like gradients w. arxiv pytorch:star: A network of deep neural networks for distant speech recognition. Thus Bayesian Networks provide a compact representation for dealing with uncertainty using an underlying graphical structure and the probability theory. ZhuSuan is a python probabilistic programming library for Bayesian deep learning, which conjoins the complimentary advantages of Bayesian methods and deep learning. Bayesian Networks do not necessarily follow Bayesian Methods, but they are named after Bayes' Rule. guided Continual Bayesian Neural Networks (UCB), where the learning rate adapts according to the uncertainty deﬁned in the probability distribution of the weights in networks. Module super class within PyTorch. on Empirical Methods in Natural Language Processing (EMNLP), 2017 Oral. Finally, you will apply transfer learning to satellite images to predict economic activity and use reinforcement learning to build agents that learn to trade in the OpenAI Gym. By unrolling we simply mean that we write out the network for the complete sequence.
calculations in our network. 3 Deep Knowledge Tracing We believe that human learning is governed by many diverse properties – of the material, the context, the timecourse of presentation, and the individual involved – many of which are difﬁcult to quantify. The implementation follows Yarin Gal's papers "Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning" (see BDropout) and "Concrete Dropout" (see CDropout). Next, you’ll learn about Convolutional Neural Networks (CNN) through an example of image recognition, where you’ll look into images from a. At its F8 annual developer conference showcasing its exceptional AI prowess, Facebook shared how the production-ready PyTorch 1. Mathematical Foundations of Deep Learning pdf book, 5. • Develop Deep Learning models in PyTorch and Keras. By versatile, I mean we can use even neural networks. The implementation is using Pytorch Paszke et al. With neural networks in PyTorch (and TensorFlow) though, it takes a lot more code than that. Approximate inference for Bayesian deep neural network is a daunting task because of the large number of uncertain parameters, e. PyTorch, MXNet, Gluon etc. They can be used to boil a sequence down into a high-level understanding, to annotate sequences, and even to generate new sequences from scratch!. Variational Inference: Bayesian Neural Networks¶ PetrochukM/PyTorch-NLP Develop Your First Neural Network in Python With Keras Step-By-Step. The model runs on top of TensorFlow, and was developed by Google. Rather than the deep learning process being a black. In this tutorial, we use the MNIST dataset and some standard PyTorch examples to show a synthetic problem where the input to the objective function is a 28 x 28 image.
Kingma, Max Welling. Neural Network Tools: Converter, Constructor and Analyser For caffe, pytorch, tensorflow, draknet and so on. Machine Learning Artificial Intelligence Python PyTorch TensorFlow Data Analysis Data Code. 2019-05-02: pytorch: public: PyTorch is an optimized tensor library for deep learning using GPUs and CPUs. Chainer is an open-source neural network framework with a Python API, whose core team of developers work at Preferred Networks, a machine-learning startup based in Tokyo drawing its engineers largely from the University of Tokyo. Further assume that p(D|θ) is the output of a neural network with weights θ. But more often, use a equal amount of data from each category in training. Therefore a Bayesian neural network is created when we place a prior distribution over a neural network’s weights. 09% on all races, and earn 39. Abstract: Deep learning techniques have been the key to major improvements in machine learning in various domains such as image and speech recognition and machine translation. “Scalable Bayesian Learning of Recurrent Neural Networks for Language Modeling" Annual Meeting of the Association for Computational Linguistics (ACL) 2017, Oral Presentation 18. All orders are custom made and most ship worldwide within 24 hours. Build your own Bayesian Convolutional Neural Network in PyTorch. This certainly extends to more cutting-edge VI applications as well as just more flexible bayesian models. Use a random image, upload your own, search for a place, or click on one of the example images in the gallery below. Unlike existing deep learning libraries, which are mainly designed for deterministic neural networks and supervised tasks, ZhuSuan provides deep. Deep Belief Networks¶.
Sequence to Sequence Learning with Neural Networks Twin Networks: Using the Future as a Regularizer Skip RNN (blog and paper) VAE with a VampPrior Bayesian DL Generative Adversarial Networks (presentation) GANs at OpenAI Revisiting the Unreasonable Effectiveness of Data. 5 Tensor Flow. Chris is the author of two highly cited and widely adopted machine learning text books: Neural Networks for Pattern Recognition (1995) and Pattern Recognition and Machine Learning (2006). arXiv ⭐️ A New Convolutional Network-in-Network Structure and Its Applications in Skin Detection, Semantic Segmentation, and Artifact Reduction. A neural network is a computing model whose layered structure resembles the networked structure of neurons in the brain. Together both the netowrks a trained which then finally passes onto a Dense layer for further classification. Autoencoders. As well as traditional neural networks, Bayesian neural networks have typically a softmax layer to compute the class probabilities. High quality Pytorch inspired T-Shirts, Posters, Mugs and more by independent artists and designers from around the world. CSC 321 Winter 2018 Intro to Neural Networks and Machine Learning. Building neural networks wasn't just easy, it was fun. Reading Time: 4 minutes Trained MLP with 2 hidden layers and a sine prior. Generative adversarial networks Building a deep generative model of MNIST digits. A Neural Autoregressive Approach to Collaborative Filtering ement given the other elements to its left in the binary vector, where all conditionals share the same parameters. Introducing TensorFlow Probability. Build models and algorithms by using different libraries such as TensorFlow, PyTorch, and Keras. For the better comprehension of autoencoders, I will present some code alongside with the explanation.
tively formulating a neural network model that can learn to perform a high-dimensional distribution-to-distribution re-gression by ingesting vast amount of examples available in our data. IBM Research - Ireland Internship Project 2019: Automated Data Science and Deep Neural Network Synthesis - overview. The approach is rather to have the network predict a single output value, the network is to predict an entire probability distribution for the output. pytorch-nightly-cpu: A lightweight library to help with training neural networks in PyTorch. Perform basic operations on your dataset using tensors and variables; Build artificial neural networks in Python with GPU acceleration; See how CNN works in PyTorch with a simple computer vision example. The policy cycles the learning rate between two boundaries with a constant frequency, as detailed in the paper Cyclical Learning Rates for Training Neural Networks. Thus a deep markov model: we allow for the transition probabilities governing the dynamics of the latent variables as well as the the emission probabilities that govern how the observations are generated by the latent dynamics to be parameterized by (non-linear) neural networks. In Neural Networks and deep neural networks what does label-dropout mean If you take the following sentence from an article on deep neural networks to regularize the classifier layer by estimating the marginalized effect of label-dropout during training. Thus Bayesian Networks provide a compact representation for dealing with uncertainty using an underlying graphical structure and the probability theory. underlying neural networks. They're at the heart of production systems at companies like Google and Facebook for face recognition, speech-to-text, and language understanding. Fb these days introduced the open supply free up of Deep Finding out Advice Fashion (DLRM), a cutting-edge AI type for serving up personalised ends up in manufacturing environments. By normalizing the output of a Softplus function in the final layer, we estimate aleatoric and epistemic uncertainty in a coherent manner. Polynomial fitting, classification, and mixture density networks will be discussed along with coding details for replications of results found in the literature. Finally, you will apply transfer learning to satellite images to predict economic activity and use reinforcement learning to build agents that learn to trade in the OpenAI Gym. recent combination of Bayesian Optimization and HyperBand, called BOHB, and uses PyTorch as DL framework. This can leave the user with a so-what feeling about Bayesian inference.
What You Will Learn • Master tensor operations for dynamic graph-based calculations using PyTorch. Facebook introduced PyTorch in 2017, and since then it has been well-received by developers. 0 is being adopted by the community and also the release of PyTorch 1. Our simple neural network model is designed to perform this high-dimensional map from a distribution over positions to a distribution over skills. Code: PyTorch | Torch. 2019-05-02: pytorch: public: PyTorch is an optimized tensor library for deep learning using GPUs and CPUs. In particular, PyTorch adopted a more dynamic and "pythonic" approach to building neural networks that's made it easier and more intuitive for Python's large community developers and data scientists. Pyro itself brings together the best of modern deep learning, Bayesian modeling, and software abstraction: it is a modern, universal, deep probabilistic programming language. The lectures cover artificial neural networks (deep learning), reinforcement learning, Bayesian modeling, model comparison and fitting, classification, probabilistic graphical models, and program induction. Ting Chen, Song Bian and Yizhou Sun; Bayesian Graph Convolutional Neural Networks using Non-parametric Graph Learning. A prototyp- ical example of this is the one-shot learning set- ting, in which we must correctly make predic- tions given only a single example of each new class. Get more data here". They now recognize images and voice at levels comparable to humans. Neill, and E. You will see how convolutional neural networks, deep neural networks, and recurrent neural networks work using PyTorch. The main competitor to Keras at this point in time is PyTorch, developed by Facebook. python) and should have a pre-existing working knowledge of probability, statistics, algorithms, and linear algebra.
PyData Warsaw 2018 We will show how to assess the uncertainty of deep neural networks. Neural network is a parameterized function Use a neural network to model the probability Parameters θ are weights of neural net. 1-release 0. Workplan and practical information. the result is uncertainty. The 2018 GitHub Octoverse report last fall named PyTorch one of the most popular open source projects on the GitHub platform, used by 31 million developers worldwide. vae-clustering Unsupervised clustering with (Gaussian mixture) VAEs Tutorial_BayesianCompressionForDL A tutorial on "Bayesian Compression for Deep Learning" published at NIPS (2017). Note that we will use Pytorch to build and train our model. In this course we study the theory of deep learning, namely of modern, multi-layered neural networks trained on big data. May 01, 2019 · PyTorch 1. Bayesian Neural Network. Briefly, suppose you have a regular neural network for regression — meaning the output is a single numeric value. The conventional convolutional layer uses linear filters followed by a nonlinear activation function to scan the input. Hyperparameters Optimization in Deep Convolutional Neural Network / Bayesian Approach with Gaussian Process Prior. But enough about who, what, and where, let's better get started. Hinton, Srivastava, Swersky, Coursera course, Neural networks for machine learning videos. Recurrent neural networks (RNNs) stand at the forefront of many recent developments in deep learning. 1 Laplace Approximations for Bayesian Neural Networks All three standard techniques for approximate inference can be applied to Bayesian neural networks and deep learning. Bayesian neural networks. The most common choice is a n l-layered network where layer 1 is the input layer, layer n.
Read the Docs v: stable. Implement deep learning models in Python using the PyTorch library and train them with real-world. Evaluate, in the context of a case study, the advantages and disadvantages of deep learning neural network architectures and other approaches. QuébecAI has 3,569 members. recent combination of Bayesian Optimization and HyperBand, called BOHB, and uses PyTorch as DL framework. 2 Requirements Good knowledge of Pytorch or Tensor ow and especially Python. Making them Bayesian with variational inference should also help with smaller samples (like less than 1000 or 10000 data points). The talk will include. Pyro is a universal probabilistic programming language (PPL) written in Python and supported by PyTorch on the backend. R2N2: Residual Recurrent Neural Networks for Multivariate Time Series Forecasting. ALVINN is a precursor to DAVE, and it provided the initial proof of concept that an end-to-end trained neural network might one day be capable of steering a car on public roads. BoTorch advances the state of the art in Bayesian optimization research by leveraging the features of PyTorch, including auto-differentiation, massive parallelism, and deep learning. Andrew Gordon Wilson I'm extremely excited to see BoTorch released: scalable, modular, and flexible Bayesian optimization, integrated with GPyTorch! It's been wonderful working with @eytan and his team. In this tutorial we will Implement Neural Network using PyTorch and understand some of the core concepts of PyTorch. bayesian-inference bayesian-neural-networks convolutional-neural-networks pytorch super-resolution bayesian bayesian-convnets Python Updated Oct 4, 2018 adiIspas / Bayesian-Neural-Network. A PyTorch implementation will be available as a plug-and-play optimiser. May 01, 2019 · PyTorch 1.
Bayesian inference problem, MCMC and variational inference Open source feature visualisation toolkit for neural networks in PyTorch. Pyro enables flexible and expressive deep probabilistic modeling, unifying the best of modern deep learning and Bayesian modeling. Turns out, the exact features that make PyTorch great also make it an excellent choice as a backend for a Bayesian data analysis librarie. ), Ohio State Board of Registration of Professional Engineers and Surveyors , USA. On the theoretical side, we cast dropout network training as approximate inference in Bayesian neural networks. Diederik P. Regularisation/model selection. MacKay, 2003. In this tutorial we will Implement Neural Network using PyTorch and understand some of the core concepts of PyTorch. We will be using pytorch for this tutorial along with several standard python packages. techniques for learning and prediction for Bayesian networks exist [Hinton and van Camp, 1993, Blundell et al. Unlike existing deep learning libraries, which are mainly designed for deterministic neural networks and supervised tasks, ZhuSuan provides deep. Feedforward neural nets model p(y|x, θ) as a nonlinear function of θ and x. An open source deep learning platform that provides a seamless path from research prototyping to production deployment. If you have studied the concept of regularization in machine learning, you will have a fair idea that regularization penalizes the coefficients. Polynomial fitting, classification, and mixture density networks will be discussed along with coding details for replications of results found in the literature. arxiv Improving Generalization Performance by Switching from Adam to SGD. Bayesian optimization is better, because it makes smarter decisions.
This concept is quite powerful, and can be employed many. The goal of this course is getting familiar with this framework and offer a guided learning for pytorch for beginners to help you creating our own deep neural networks - a multilayer perceptron and a convolutional neural network for image classification. A simple 2 hidden layer siamese network for binary classiﬁcation with logistic prediction p. These limitations were overcome by advances that allowed neural networks to discover internal representations, leading to another wave of enthusiasm in the late 1980s. 2-release Downloads pdf. Let an algorithm tell you how to eat. I heard an interesting talk recently about Bayesian neural networks (BNNs). In Neural Networks and deep neural networks what does label-dropout mean If you take the following sentence from an article on deep neural networks to regularize the classifier layer by estimating the marginalized effect of label-dropout during training. 56 MB, 97 pages and we collected some download links, you can download this pdf book for free. 1 comes with new APIs, support for Boolean tensors and custom recurrent neural networks, and an upgrade of the JIT compiler for optimizing computational graphs. In probability model terms, the inference network parametrizes the approximate posterior of the latent variables. 2019-05-02: ignite: public. Bayesian optimization is better, because it makes smarter decisions. 1-release 0. The problem that both Convolutional Neural Networks and Recurrent Neural Networks solve is constructing an efficient neural network for the case where the size of the input is large or unrestricted. In particular, PyTorch adopted a more dynamic and "pythonic" approach to building neural networks that's made it easier and more intuitive for Python's large community developers and data scientists. pytorch/pytorch: Tensors and Dynamic neural networks in Python with strong GPU acceleration; pytorch/pytorch: Tensors and Dynamic neural networks in Python with.
Standard NN training via optimization is (from a probabilistic perspective) equivalent to maximum likelihood estimation (MLE) for the weights. To sum up, our Adv-BNN method trains an arbitrary Bayesian neural network with the adversarial examples of the same model, which is similar to Madry et al. A recurrent neural network (RNN) is a class of artificial neural networks where connections between nodes form a directed graph along a temporal sequence. This concept is quite powerful, and can be employed many. In manymultivariate time series modeling problems, there is usually a significantlinear dependency component, for which VARs are suitable, and a nonlinearcomponent, for which RNNs are suitable. Writing your first Bayesian Neural Network in Pyro and PyTorch. edu Abstract We combine various state of the art approaches to train-ing deep convolutional neural networks to achieve the best performance possible on the Tiny ImageNet dataset. Pyro enables flexible and expressive deep probabilistic modeling, unifying the best of modern deep learning and Bayesian modeling. BoTorch is a PyTorch-based Bayesian optimization library aimed at researchers creating black-box functions, and Ax is a brand-new open source, modular platform for machine learning that allows for plug-and-play algorithms and A/B testing. Neural Networks and Deep Learning: A Textbook This book covers both classical and modern models in deep learning. Sharing concepts, ideas, and codes. In short, the Bayesian approach depends on both prior distribution and likelihood function, while the frequentist approach depends only on the likelihood function. Today: gradients of neural network parameters via the backpropagationof gradients algorithm. PyData Warsaw 2018 We will show how to assess the uncertainty of deep neural networks. The emerging research area of Bayesian Deep Learning seeks to combine the benefits of modern deep learning methods (scalable gradient-based training of flexible neural networks for regression and classification) with the benefits of modern Bayesian statistical methods to estimate probabilities and make decisions under uncertainty. 77% on specific race classes. Learn Improving Deep Neural Networks: Hyperparameter tuning, Regularization and Optimization from deeplearning.
One added benefit of pytorch is that they are aiming to support an interface where pytorch is a clean drop-in replacement for numpy i. Native GPU & autograd support. , 2015, Gal and Ghahramani, 2016]. Model Pruning in a Bayesian Neural Network. This work enables practical deep learning while preserving benefits of Bayesian principles. In case you're new to either of these, I recommend following resources: Bayesian Methods for Hackers to learn the basics of Bayesian modeling and probabilistic programming. In our surrogate problem, the task is to find a high-dimensional posterior distribution over millions of random variables using less than hundreds or thousands. Making a neural network say “I Don’t Know”: Bayesian NNs using Pyro and PyTorch This works if you get nicely balanced probabilities out of neural network. Further assume that p(D|θ) is the output of a neural network with weights θ. Alrao was inspired by the intuition that not all units in a neural network end up being useful. Workplan and practical information. The model runs on top of TensorFlow, and was developed by Google. Bayesian Neural Network. The model offers better robustness to over-fitting on small data and achieves a considerable improvement in classification accuracy compared to previous approaches. 2019-05-02: pytorch: public: PyTorch is an optimized tensor library for deep learning using GPUs and CPUs. Herlands, A. Finally, you will apply transfer learning to satellite images to predict economic activity and use reinforcement learning to build agents that learn to trade in the OpenAI Gym. We are looking to expand our deep learning team to advance the state of the art and contribute to our ongoing commercial engagements in manufacturing. Key words: Neural network, estimation, lines of code, function point INTRODUCTION The estimation of resource expenditure (example, effort, schedule ) is an essential software project management activity. By contrast, a Bayesian neural network predicts a distribution of values; for example, a model predicts a house price of 853,000 with a standard deviation of 67,200. Bayesian Neural Network Pytorch.