DOCSLIB.ORG

Multilayer Perceptron (MLP) Application Guidelines

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Multilayer Perceptron (MLP) Application Guidelines Contents Introduction How to use MLPs NN Design Case Study I: Classification Case Study II: Regression Case Study III: Reinforcement Learning Multilayer Perceptron (MLP) Application Guidelines Paulo Cortez [email protected] http://www.dsi.uminho.pt/~pcortez Departamento de Sistemas de Informa¸c˜ao University of Minho - Campus de Azur´em 4800-058 Guimar˜aes - Portugal Paulo Cortez Multilayer Perceptron (MLP)Application Guidelines Contents Introduction How to use MLPs NN Design Case Study I: Classification Case Study II: Regression Case Study III: Reinforcement Learning 1 Introduction 2 How to use MLPs 3 NN Design 4 Case Study I: Classification 5 Case Study II: Regression 6 Case Study III: Reinforcement Learning Paulo Cortez Multilayer Perceptron (MLP)Application Guidelines Contents Introduction How to use MLPs NN Design Case Study I: Classification Case Study II: Regression Case Study III: Reinforcement Learning Node Activation Further information in [Bishop, 1995] and [Sarle, 2003]. Each node outputs an activation function applied over the P weighted sum of its inputs: si = f (wi,0 + j∈I wi,j × sj ) x = +1 0 w = Bias x i0 1 w i1 x Node 2 w i2 i n Inputs ... Σ f ui si w in xn Paulo Cortez Multilayer Perceptron (MLP)Application Guidelines Contents Introduction How to use MLPs NN Design Case Study I: Classification Case Study II: Regression Case Study III: Reinforcement Learning Activation functions Linear: y = x ; Tanh: y = tanh(x); 1 Logistic (or sigmoid): y = 1+e−x ; 1 0 −4 −2 0 2 4 Paulo Cortez Multilayer Perceptron (MLP)Application Guidelines Contents Introduction How to use MLPs NN Design Case Study I: Classification Case Study II: Regression Case Study III: Reinforcement Learning Only feedforward connections exist; Nodes are organized in layers; Input Hidden Hidden Output Layer Layer Layer Layer 3 shortcut 7 1 4 6 2 bias 8 shortcut 5 Paulo Cortez Multilayer Perceptron (MLP)Application Guidelines Contents Introduction How to use MLPs NN Design Case Study I: Classification Case Study II: Regression Case Study III: Reinforcement Learning Why MLPs? Popularity - the most used type of NN; Universal Approximators - general-purpose models, with a huge number of applications; Nonlinearity - capable of modeling complex functions; Robustness - good at ignoring irrelevant inputs and noise; Adaptability - can adapt its weights and/or topology in response to environment changes; Easy of Use - black-box point of view, can be used with few knowledge about the relationship of the function to be modeled. Paulo Cortez Multilayer Perceptron (MLP)Application Guidelines Contents Introduction How to use MLPs NN Design Case Study I: Classification Case Study II: Regression Case Study III: Reinforcement Learning Who is interested in MLPs? Computer Scientists : study properties of non-symbolic information processing; Statisticians: perform flexible data analysis; Engineers: exploit MLP capabilities in several areas; Cognitive Scientists: describe models of thinking; Biologists: interpret DNA sequences; ... Paulo Cortez Multilayer Perceptron (MLP)Application Guidelines Contents Introduction How to use MLPs NN Design Case Study I: Classification Case Study II: Regression Case Study III: Reinforcement Learning Applications [Cortez et al., 2002] Supervised Learning (Input/Output Mapping): Classification (discrete outputs): Diabetes in Pima Indians; Sonar: Rocks vs Mines; Regression (numeric outputs): Prognostic Breast Cancer; Pumadyn Robot Arm; Reinforcement Learning (Output is not perfectly known): Control (e.g., autonomous driving); Game Playing (e.g., checkers); Paulo Cortez Multilayer Perceptron (MLP)Application Guidelines Contents Introduction How to use MLPs NN Design Case Study I: Classification Case Study II: Regression Case Study III: Reinforcement Learning Software [Sarle, 2003] Commercial: SAS Enterprise Miner Software; MATLAB Neural Network Toolbox; STATISTICA: Neural Networks; Clementine http://www.spss.com/spssbi/clementine/index.htm; Free: Stuttgart Neural Network Simulator (SNNS) (C code source); Joone: Java Object Oriented Neural Engine (code source); R (statistical tool) http://www.r-project.org/; WEKA (data mining) http://www.cs.waikato.ac.nz/~ml/weka/; Built Your Own: Better control, but take caution! Paulo Cortez Multilayer Perceptron (MLP)Application Guidelines Contents Introduction How to use MLPs NN Design Case Study I: Classification Case Study II: Regression Case Study III: Reinforcement Learning Classification Metrics The confusion matrix [Kohavi & Provost, 1998] matches the predicted and actual values; Table: The 2 × 2 confusion matrix. ↓ actual \ predicted → negative positive negative TN FP positive FN TP Three accuracy measures can be defined: TP the Sensitivity (Type II Error) = FN+TP × 100 (%) ; TN the Specificity (Type I Error) ; = TN+FP × 100 (%) TN+TP the Accuracy = TN+FP+FN+TP × 100 (%) ; Paulo Cortez Multilayer Perceptron (MLP)Application Guidelines Contents Introduction How to use MLPs NN Design Case Study I: Classification Case Study II: Regression Case Study III: Reinforcement Learning Regression The error e is given by: e = d − db where d denotes the desired value and the db estimated value (given by the model); Given a dataset with the function pairs x1 → d1, ··· , xN → dN , we can compute: PN i=1|ei | Mean Absolute Deviation (MAD): MAD = N PN 2 Sum Squared Error (SSE): SSE = i=1 ei Mean Squared Error (MSE): MSE = SSE N √ Root Mean Squared Error (RMSE): RMSE = MSE Correlation metrics (scale independent): Person [-1, 1]; P 2 2 (y−by) Press r squared: R = 1 − P(y−y)2 Paulo Cortez Multilayer Perceptron (MLP)Application Guidelines Contents Introduction How to use MLPs NN Design Case Study I: Classification Case Study II: Regression Case Study III: Reinforcement Learning Data Collection and Preprocessing Learning samples must be representative, hundreds or thousands of cases are required; Only numeric values can be fed (discretization); Treat missing values (delete or substitute); Rescaling: inputs: x−(max+min)/2 y = (max−min)/2 (maximum–mininum: range [-1,1]) x−x y = s (Mahalanobis scaling: mean 0 and std 1) numeric outputs: within [0,1] if logistic and [-1,1] if tanh. (x−min) y = max−min (maximum–mininum: range [0, 1]) Paulo Cortez Multilayer Perceptron (MLP)Application Guidelines Contents Introduction How to use MLPs NN Design Case Study I: Classification Case Study II: Regression Case Study III: Reinforcement Learning Nominal variables (with 2 or more non-ordered classes): 1-of-C coding: use one binary variable per class; Color example: Blue - 1 0 0, Red - 0 1 0, Green - 0 0 1. x Paulo Cortez Multilayer Perceptron (MLP)Application Guidelines Contents Introduction How to use MLPs NN Design Case Study I: Classification Case Study II: Regression Case Study III: Reinforcement Learning Consult [Flexer, 1996] for further details. Holdout, split the data into two exclusive sets, using random sampling: training: used to set the MLP weights (2/3); test: used to infer the MLP performance (1/3). K-fold, works as above but uses rotation: data is split into K exclusive folds of equal size; each part is used as a test set, being the rest used for training; the overall performance is measured by averaging the K runs results; 10-fold most used if hundreds of examples; leave-one-out (N-fold) used if less than 100 or 200 examples; Third extra set is needed if parameter tunning; Paulo Cortez Multilayer Perceptron (MLP)Application Guidelines Contents Introduction How to use MLPs NN Design Case Study I: Classification Case Study II: Regression Case Study III: Reinforcement Learning Training Algorithms Gradient-descent (O(n)) [Riedmiller, 1994]: Backpropagation (BP) - most used, yet slow; Backpropagation with Momentum - faster than BP, requires additional parameter tunning; QuickProp - faster than BP with Momentum; RPROP - faster than QuickProp and stable in terms of its internal parameters; Levenberg-Marquardt One of the most accurate algorithms; O(n2) in terms of computer (memory, speed) requirements (use with small networks); Paulo Cortez Multilayer Perceptron (MLP)Application Guidelines Contents Introduction How to use MLPs NN Design Case Study I: Classification Case Study II: Regression Case Study III: Reinforcement Learning Overfitting Output B A Training Data Test Data Input If possible use large datasets: N p (weights); Model Selection - apply several models and then choose the one with the best generalization estimate; Regularization - use learning penalties or restrictions: Early stopping - stop when the estimate arises; Weight decay - in each epoch slightly decrease the weights; Jitter - training with added noise. Paulo Cortez Multilayer Perceptron (MLP)Application Guidelines Contents Introduction How to use MLPs NN Design Case Study I: Classification Case Study II: Regression Case Study III: Reinforcement Learning MLP Capabilities Linear learning when: there are no hidden layers; or only linear activation functions are used. Nonlinear learning: any continuous function mapping can be learned with one hidden layer; discontinuous complex functions can be learned with more hidden layers. It is better to perform only one classification/regression task per network; i.e., use C/1 output node(s). Activation Functions: Hidden Nodes: use the logistic (or tanh); Output Nodes: if outputs bounded, apply the same function; else use the linear function; Paulo Cortez Multilayer Perceptron (MLP)Application Guidelines Contents Introduction How to use MLPs NN Design Case Study I: Classification Case Study II: Regression Case Study III: Reinforcement Learning
Load more

Recommended publications
  • Audio Event Classification Using Deep Learning in an End-To-End Approach
    Audio Event Classification using Deep Learning in an End-to-End Approach Master thesis Jose Luis Diez Antich Aalborg University Copenhagen A. C. Meyers Vænge 15 2450 Copenhagen SV Denmark Title: Abstract: Audio Event Classification using Deep Learning in an End-to-End Approach The goal of the master thesis is to study the task of Sound Event Classification Participant(s): using Deep Neural Networks in an end- Jose Luis Diez Antich to-end approach. Sound Event Classifi- cation it is a multi-label classification problem of sound sources originated Supervisor(s): from everyday environments. An auto- Hendrik Purwins matic system for it would many applica- tions, for example, it could help users of hearing devices to understand their sur- Page Numbers: 38 roundings or enhance robot navigation systems. The end-to-end approach con- Date of Completion: sists in systems that learn directly from June 16, 2017 data, not from features, and it has been recently applied to audio and its results are remarkable. Even though the re- sults do not show an improvement over standard approaches, the contribution of this thesis is an exploration of deep learning architectures which can be use- ful to understand how networks process audio. The content of this report is freely available, but publication (with reference) may only be pursued due to agreement with the author. Contents 1 Introduction1 1.1 Scope of this work.............................2 2 Deep Learning3 2.1 Overview..................................3 2.2 Multilayer Perceptron...........................4
    [Show full text]
  • 4 Nonlinear Regression and Multilayer Perceptron
    4 Nonlinear Regression and Multilayer Perceptron In nonlinear regression the output variable y is no longer a linear function of the regression parameters plus additive noise. This means that estimation of the parameters is harder. It does not reduce to minimizing a convex energy functions { unlike the methods we described earlier. The perceptron is an analogy to the neural networks in the brain (over-simplified). It Pd receives a set of inputs y = j=1 !jxj + !0, see Figure (3). Figure 3: Idealized neuron implementing a perceptron. It has a threshold function which can be hard or soft. The hard one is ζ(a) = 1; if a > 0, ζ(a) = 0; otherwise. The soft one is y = σ(~!T ~x) = 1=(1 + e~!T ~x), where σ(·) is the sigmoid function. There are a variety of different algorithms to train a perceptron from labeled examples. Example: The quadratic error: t t 1 t t 2 E(~!j~x ; y ) = 2 (y − ~! · ~x ) ; for which the update rule is ∆!t = −∆ @E = +∆(yt~! · ~xt)~xt. Introducing the sigmoid j @!j function rt = sigmoid(~!T ~xt), we have t t P t t t t E(~!j~x ; y ) = − i ri log yi + (1 − ri) log(1 − yi ) , and the update rule is t t t t ∆!j = −η(r − y )xj, where η is the learning factor. I.e, the update rule is the learning factor × (desired output { actual output)× input. 10 4.1 Multilayer Perceptrons Multilayer perceptrons were developed to address the limitations of perceptrons (introduced in subsection 2.1) { i.e.
    [Show full text]
  • Petroleum and Coal
    Petroleum and Coal Article Open Access IMPROVED ESTIMATION OF PERMEABILITY OF NATURALLY FRACTURED CARBONATE OIL RESER- VOIRS USING WAVENET APPROACH Mohammad M. Bahramian 1, Abbas Khaksar-Manshad 1*, Nader Fathianpour 2, Amir H. Mohammadi 3, Bengin Masih Awdel Herki 4, Jagar Abdulazez Ali 4 1 Department of Petroleum Engineering, Abadan Faculty of Petroleum Engineering, Petroleum University of Technology (PUT), Abadan, Iran 2 Department of Mining Engineering, Isfahan University of Technology, Isfahan, Iran 3 Discipline of Chemical Engineering, School of Engineering, University of KwaZulu-Natal, Howard College Campus, King George V Avenue, Durban 4041, South Africa 4 Faculty of Engineering, Soran University, Kurdistan-Iraq Received June 18, 2017; Accepted September 30, 2017 Abstract One of the most important parameters which is regarded in petroleum industry is permeability that its accurate knowledge allows petroleum engineers to have adequate tools to evaluate and minimize the risk and uncertainty in the exploration of oil and gas reservoirs. Different direct and indirect methods are used to measure this parameter most of which (e.g. core analysis) are very time -consuming and cost consuming. Hence, applying an efficient method that can model this important parameter has the highest importance. Most of the researches show that the capability (i.e. classification, optimization and data mining) of an Artificial Neural Network (ANN) is suitable for imperfections found in petroleum engineering problems considering its successful application. In this study, we have used a Wavenet Neural Network (WNN) model, which was constructed by combining neural network and wavelet theory to improve estimation of permeability. To achieve this goal, we have also developed MLP and RBF networks and then compared the results of the latter two networks with the results of WNN model to select the best estimator between them.
    [Show full text]
  • Learning Sabatelli, Matthia; Loupe, Gilles; Geurts, Pierre; Wiering, Marco
    View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by University of Groningen University of Groningen Deep Quality-Value (DQV) Learning Sabatelli, Matthia; Loupe, Gilles; Geurts, Pierre; Wiering, Marco Published in: ArXiv IMPORTANT NOTE: You are advised to consult the publisher's version (publisher's PDF) if you wish to cite from it. Please check the document version below. Document Version Early version, also known as pre-print Publication date: 2018 Link to publication in University of Groningen/UMCG research database Citation for published version (APA): Sabatelli, M., Loupe, G., Geurts, P., & Wiering, M. (2018). Deep Quality-Value (DQV) Learning. ArXiv. Copyright Other than for strictly personal use, it is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license (like Creative Commons). Take-down policy If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim. Downloaded from the University of Groningen/UMCG research database (Pure): http://www.rug.nl/research/portal. For technical reasons the number of authors shown on this cover page is limited to 10 maximum. Download date: 19-05-2020 Deep Quality-Value (DQV) Learning Matthia Sabatelli Gilles Louppe Pierre Geurts Montefiore Institute Montefiore Institute Montefiore Institute Université de Liège, Belgium Université de Liège, Belgium Université de Liège, Belgium [email protected] [email protected] [email protected] Marco A.
    [Show full text]
  • The Architecture of a Multilayer Perceptron for Actor-Critic Algorithm with Energy-Based Policy Naoto Yoshida
    The Architecture of a Multilayer Perceptron for Actor-Critic Algorithm with Energy-based Policy Naoto Yoshida To cite this version: Naoto Yoshida. The Architecture of a Multilayer Perceptron for Actor-Critic Algorithm with Energy- based Policy. 2015. hal-01138709v2 HAL Id: hal-01138709 https://hal.archives-ouvertes.fr/hal-01138709v2 Preprint submitted on 19 Oct 2015 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. The Architecture of a Multilayer Perceptron for Actor-Critic Algorithm with Energy-based Policy Naoto Yoshida School of Biomedical Engineering Tohoku University Sendai, Aramaki Aza Aoba 6-6-01 Email: [email protected] Abstract—Learning and acting in a high dimensional state- when the actions are represented by binary vector actions action space are one of the central problems in the reinforcement [4][5][6][7][8]. Energy-based RL algorithms represent a policy learning (RL) communities. The recent development of model- based on energy-based models [9]. In this approach the prob- free reinforcement learning algorithms based on an energy- based model have been shown to be effective in such domains. ability of the state-action pair is represented by the Boltzmann However, since the previous algorithms used neural networks distribution and the energy function, and the policy is a with stochastic hidden units, these algorithms required Monte conditional probability given the current state of the agent.
    [Show full text]
  • Performance Analysis of Multilayer Perceptron in Profiling Side
    Performance Analysis of Multilayer Perceptron in Profiling Side-channel Analysis L´eoWeissbart1;2 1 Delft University of Technology, The Netherlands 2 Digital Security Group, Radboud University, The Netherlands Abstract. In profiling side-channel analysis, machine learning-based analysis nowadays offers the most powerful performance. This holds espe- cially for techniques stemming from the neural network family: multilayer perceptron and convolutional neural networks. Convolutional neural net- works are often favored as results suggest better performance, especially in scenarios where targets are protected with countermeasures. Mul- tilayer perceptron receives significantly less attention, and researchers seem less interested in this method, narrowing the results in the literature to comparisons with convolutional neural networks. On the other hand, a multilayer perceptron has a much simpler structure, enabling easier hyperparameter tuning and, hopefully, contributing to the explainability of this neural network inner working. We investigate the behavior of a multilayer perceptron in the context of the side-channel analysis of AES. By exploring the sensitivity of mul- tilayer perceptron hyperparameters over the attack's performance, we aim to provide a better understanding of successful hyperparameters tuning and, ultimately, this algorithm's performance. Our results show that MLP (with a proper hyperparameter tuning) can easily break im- plementations with a random delay or masking countermeasures. This work aims to reiterate the power of simpler neural network techniques in the profiled SCA. 1 Introduction Side-channel analysis (SCA) exploits weaknesses in cryptographic algorithms' physical implementations rather than the mathematical properties of the algo- rithms [16]. There, SCA correlates secret information with unintentional leakages like timing [13], power dissipation [14], and electromagnetic (EM) radiation [25].
    [Show full text]
  • Perceptron 1 History of Artificial Neural Networks
    Introduction to Machine Learning (Lecture Notes) Perceptron Lecturer: Barnabas Poczos Disclaimer: These notes have not been subjected to the usual scrutiny reserved for formal publications. They may be distributed outside this class only with the permission of the Instructor. 1 History of Artificial Neural Networks The history of artificial neural networks is like a roller-coaster ride. There were times when it was popular(up), and there were times when it wasn't. We are now in one of its very big time. • Progression (1943-1960) { First Mathematical model of neurons ∗ Pitts & McCulloch (1943) [MP43] { Beginning of artificial neural networks { Perceptron, Rosenblatt (1958) [R58] ∗ A single neuron for classification ∗ Perceptron learning rule ∗ Perceptron convergence theorem [N62] • Degression (1960-1980) { Perceptron can't even learn the XOR function [MP69] { We don't know how to train MLP { 1963 Backpropagation (Bryson et al.) ∗ But not much attention • Progression (1980-) { 1986 Backpropagation reinvented: ∗ Learning representations by back-propagation errors. Rumilhart et al. Nature [RHW88] { Successful applications in ∗ Character recognition, autonomous cars, ..., etc. { But there were still some open questions in ∗ Overfitting? Network structure? Neuron number? Layer number? Bad local minimum points? When to stop training? { Hopfield nets (1982) [H82], Boltzmann machines [AHS85], ..., etc. • Degression (1993-) 1 2 Perceptron: Barnabas Poczos { SVM: Support Vector Machine is developed by Vapnik et al.. [CV95] However, SVM is a shallow architecture. { Graphical models are becoming more and more popular { Great success of SVM and graphical models almost kills the ANN (Artificial Neural Network) research. { Training deeper networks consistently yields poor results. { However, Yann LeCun (1998) developed deep convolutional neural networks (a discriminative model).
    [Show full text]
  • TF-IDF Vs Word Embeddings for Morbidity Identification in Clinical Notes: an Initial Study
    TF-IDF vs Word Embeddings for Morbidity Identification in Clinical Notes: An Initial Study 1 2 Danilo Dess`ı [0000−0003−3843−3285], Rim Helaoui [0000−0001−6915−8920], Vivek 1 1 Kumar [0000−0003−3958−4704], Diego Reforgiato Recupero [0000−0001−8646−6183], and 1 Daniele Riboni [0000−0002−0695−2040] 1 University of Cagliari, Cagliari, Italy {danilo dessi, vivek.kumar, diego.reforgiato, riboni}@unica.it 2 Philips Research, Eindhoven, Netherlands [email protected] Abstract. Today, we are seeing an ever-increasing number of clinical notes that contain clinical results, images, and textual descriptions of pa-tient’s health state. All these data can be analyzed and employed to cater novel services that can help people and domain experts with their com-mon healthcare tasks. However, many technologies such as Deep Learn-ing and tools like Word Embeddings have started to be investigated only recently, and many challenges remain open when it comes to healthcare domain applications. To address these challenges, we propose the use of Deep Learning and Word Embeddings for identifying sixteen morbidity types within textual descriptions of clinical records. For this purpose, we have used a Deep Learning model based on Bidirectional Long-Short Term Memory (LSTM) layers which can exploit state-of-the-art vector representations of data such as Word Embeddings. We have employed pre-trained Word Embeddings namely GloVe and Word2Vec, and our own Word Embeddings trained on the target domain. Furthermore, we have compared the performances of the deep learning approaches against the traditional tf-idf using Support Vector Machine and Multilayer per-ceptron (our baselines).
    [Show full text]
  • Multilayer Perceptron
    Advanced Introduction to Machine Learning, CMU-10715 Perceptron, Multilayer Perceptron Barnabás Póczos, Sept 17 Contents History of Artificial Neural Networks Definitions: Perceptron, MLP Representation questions Perceptron algorithm Backpropagation algorithm 2 Short History Progression (1943-1960) • First mathematical model of neurons . Pitts & McCulloch (1943) • Beginning of artificial neural networks • Perceptron, Rosenblatt (1958) . A single layer neuron for classification . Perceptron learning rule . Perceptron convergence theorem Degression (1960-1980) • Perceptron can’t even learn the XOR function • We don’t know how to train MLP • 1969 Backpropagation… but not much attention… 3 Short History Progression (1980-) • 1986 Backpropagation reinvented: . Rumelhart, Hinton, Williams: Learning representations by back-propagating errors. Nature, 323, 533—536, 1986 • Successful applications: . Character recognition, autonomous cars,… • Open questions: Overfitting? Network structure? Neuron number? Layer number? Bad local minimum points? When to stop training? • Hopfield nets (1982), Boltzmann machines,… 4 Short History Degression (1993-) • SVM: Vapnik and his co-workers developed the Support Vector Machine (1993). It is a shallow architecture. • SVM almost kills the ANN research. • Training deeper networks consistently yields poor results. • Exception: deep convolutional neural networks, Yann LeCun 1998. (discriminative model) 5 Short History Progression (2006-) Deep Belief Networks (DBN) • Hinton, G. E, Osindero, S., and Teh, Y.
    [Show full text]
  • Imputation and Generation of Multidimensional Market Data
    IMPUTATION AND GENERATION OF MULTIDIMENSIONAL MARKET DATA Master Thesis Tobias Wall & Jacob Titus Master thesis, 30 credits Department of mathematics and Mathematical Statistics Spring Term 2021 Imputation and Generation of Multidimensional Market Data Tobias Wall†, [email protected] Jacob Titus†, [email protected] Copyright © by Tobias Wall and Jacob Titus, 2021. All rights reserved. Supervisors: Jonas Nylén Nasdaq Inc. Armin Eftekhari Umeå University Examiner: Jianfeng Wang Umeå University Master of Science Thesis in Industrial Engineering and Management, 30 ECTS Department of Mathematics and Mathematical Statistics Umeå University SE-901 87 Umeå, Sweden †Equal contribution. The order of the contributors names were chosen based on a bootstrapping procedure where the names was drawn 100 times. i Abstract Market risk is one of the most prevailing risks to which financial institutions are exposed. The most popular approach in quantifying market risk is through Value at Risk. Organisations and regulators often require a long historical horizon of the affecting financial variables to estimate the risk exposures. A long horizon stresses the completeness of the available data; something risk applications need to handle. The goal of this thesis is to evaluate and propose methods to impute finan- cial time series. The performance of the methods will be measured with respect to both price-, and risk metric replication. Two different use cases are evaluated; missing values randomly place in the time series and consecutively missing values at the end-point of a time series. In total, there are five models applied to each use case, respectively. For the first use case, the results show that all models perform better than the naive approach.
    [Show full text]
  • Lecture 7. Multilayer Perceptron. Backpropagation
    Lecture 7. Multilayer Perceptron. Backpropagation COMP90051 Statistical Machine Learning Semester 2, 2017 Lecturer: Andrey Kan Copyright: University of Melbourne Statistical Machine Learning (S2 2017) Deck 7 This lecture • Multilayer perceptron ∗ Model structure ∗ Universal approximation ∗ Training preliminaries • Backpropagation ∗ Step-by-step derivation ∗ Notes on regularisation 2 Statistical Machine Learning (S2 2017) Deck 7 Animals in the zoo Artificial Neural Recurrent neural Networks (ANNs) networks Feed-forward Multilayer perceptrons networks art: OpenClipartVectors at pixabay.com (CC0) Perceptrons Convolutional neural networks • Recurrent neural networks are not covered in this subject • If time permits, we will cover autoencoders. An autoencoder is an ANN trained in a specific way. ∗ E.g., a multilayer perceptron can be trained as an autoencoder, or a recurrent neural network can be trained as an autoencoder. 3 Statistical Machine Learning (S2 2016) Deck 7 Multilayer Perceptron Modelling non-linearity via function composition 4 Statistical Machine Learning (S2 2017) Deck 7 Limitations of linear models Some function are linearly separable, but many are not AND OR XOR Possible solution: composition XOR = OR AND not AND 1 2 1 2 1 2 We are going to combine perceptrons … 5 Statistical Machine Learning (S2 2017) Deck 7 Simplified graphical representation Sputnik – first artificial Earth satellite 6 Statistical Machine Learning (S2 2017) Deck 7 Perceptorn is sort of a building block for ANN • ANNs are not restricted to binary classification
    [Show full text]
  • A Multilayer Perceptron Solution to the Match
    290 lEEE TRANSACTIONS ON KNOWLEDGE AND DATA ENGINEERING, VOL. 4, NO. 3, JUNE 1992 Concise Papers A Multilayer Perceptron Solution to the Match Phase description of the Rete Match Algorithm, the conventional solution Problem in Rule-Based Artificial Intelligence Systems to the match phase problem. A rule-based expert system uses rules, sometimes referred to as Michael A. Sartori, Kevin M. Passino, and Panos J. Antsaklis, productions or production rules, to represent knowledge and uses an inference engine to perform the actions of the expert system. In general, a rule is of the form Abstruct- In rule-based artificial intelligence (AI) planning, expert, and learning systems, it is often the case that the left-hand-sides of the IF (antecedent) THEN (consequence) (1) rules must be repeatedly compared to the contents of some “working memory.” Normally, the intent is to determine which rules are relevant Customarily, the antecedent is referred to as the left-hand-side, and to the current situation (i.e., to find the “conflict set”). The traditional approach to solve such a “match phase problem” for production systems the consequence is referred to as the right-hand-side. The working is to use the Rete Match Algorithm. Here, a new technique using a memory (data memory) contains dynamic data that is compared to multilayer perceptron, a particular artificial neural network model, is the left-hand-side of the rules. The individual elements of the working presented to solve the match phase problem for rule-based AI systems. memory are referred to as the working memory elements. The A syntax for premise formulas (i.e., the left-hand-sides of the rules) is inference engine performs the comparison of the working memory defined, and working memory is specified.
    [Show full text]