Automated Mathematical Equation Structure Discovery for Visual Analysis

Finding the best mathematical equation to deal with the different challenges found in complex scenarios requires a thorough understanding of the scenario and a trial and error process carried out by experts. In recent years, most state-of-the-art equation discovery methods have been widely applied in modeling and identification systems. However, equation discovery approaches can be very useful in computer vision, particularly in the field of feature extraction. In this paper, we focus on recent AI advances to present a novel framework for automatically discovering equations from scratch with little human intervention to deal with the different challenges encountered in real-world scenarios. In addition, our proposal can reduce human bias by proposing a search space design through generative network instead of hand-designed. As a proof of concept, the equations discovered by our framework are used to distinguish moving objects from the background in video sequences. Experimental results show the potential of the proposed approach and its effectiveness in discovering the best equation in video sequences. The code and data are available at: https://github.com/carolinepacheco/equation discovery scene analysis.

[1]  Herbert A. Simon,et al.  Scientific discovery: compulalional explorations of the creative process , 1987 .

[2]  Geoffrey E. Hinton,et al.  ImageNet classification with deep convolutional neural networks , 2012, Commun. ACM.

[3]  George Kurian,et al.  Google's Neural Machine Translation System: Bridging the Gap between Human and Machine Translation , 2016, ArXiv.

[4]  Li Fei-Fei,et al.  ImageNet: A large-scale hierarchical image database , 2009, CVPR.

[5]  Kaiming He,et al.  Exploring Randomly Wired Neural Networks for Image Recognition , 2019, 2019 IEEE/CVF International Conference on Computer Vision (ICCV).

[6]  Guandong Xu,et al.  A Boundary-aware Neural Model for Nested Named Entity Recognition , 2019, EMNLP.

[7]  Saso Dzeroski,et al.  Theory Revision in Equation Discovery , 2001, Discovery Science.

[8]  Daniel Jurafsky,et al.  First-Pass Large Vocabulary Continuous Speech Recognition using Bi-Directional Recurrent DNNs , 2014, ArXiv.

[9]  Mieczyslaw M. Kokar,et al.  Discovering Functional Formulas through Changing Representation Base , 1986, AAAI.

[10]  Saining Xie,et al.  On Network Design Spaces for Visual Recognition , 2019, 2019 IEEE/CVF International Conference on Computer Vision (ICCV).

[11]  Tara N. Sainath,et al.  Improving deep neural networks for LVCSR using rectified linear units and dropout , 2013, 2013 IEEE International Conference on Acoustics, Speech and Signal Processing.

[12]  Pat Langley,et al.  An Integrated Approach to Empirical Discovery , 1989 .

[13]  Ron Kohavi,et al.  Automatic Parameter Selection by Minimizing Estimated Error , 1995, ICML.

[14]  Yoshua Bengio,et al.  Neural Machine Translation by Jointly Learning to Align and Translate , 2014, ICLR.

[15]  N. Hansen.  A CMA-ES for Mixed-Integer Nonlinear Optimization , 2011 .

[16]  Sanjeev Khudanpur,et al.  End-to-end Speech Recognition Using Lattice-free MMI , 2018, INTERSPEECH.

[17]  B. Samanta,et al.  Gear fault detection using artificial neural networks and support vector machines with genetic algorithms , 2004 .

[18]  Aaron Klein,et al.  Hyperparameter Optimization , 2017, Encyclopedia of Machine Learning and Data Mining.

[19]  Omer Levy,et al.  BART: Denoising Sequence-to-Sequence Pre-training for Natural Language Generation, Translation, and Comprehension , 2019, ACL.

[20]  Isabelle Guyon,et al.  Analysis of the IJCNN 2007 agnostic learning vs. prior knowledge challenge , 2008, Neural Networks.

[21]  H. Simon,et al.  Heuristics for empirical discovery , 1987 .

[22]  Yoshua Bengio,et al.  Random Search for Hyper-Parameter Optimization , 2012, J. Mach. Learn. Res..

[23]  Saso Dzeroski,et al.  Discovering dynamics: From inductive logic programming to machine discovery , 1993, Journal of Intelligent Information Systems.

[24]  Brian D. Ripley,et al.  Statistical aspects of neural networks , 1993 .

[25]  M. Kokar.  Determining arguments of invariant functional descriptions , 2004, Machine Learning.

[26]  Daniel Kobler.  Evolutionary Algorithms in Combinatorial Optimization , 2009, Encyclopedia of Optimization.

[27]  Saso Dzeroski,et al.  Combinatorial search for selecting the structure of models of dynamical systems with equation discovery , 2020, Eng. Appl. Artif. Intell..

[28]  Lothar Thiele,et al.  Multiobjective Optimization Using Evolutionary Algorithms - A Comparative Case Study , 1998, PPSN.

[29]  Oriol Vinyals,et al.  Hierarchical Representations for Efficient Architecture Search , 2017, ICLR.

[30]  Zsolt Kira,et al.  Learning to cluster in order to Transfer across domains and tasks , 2017, ICLR.

[31]  Hui Wang,et al.  Multilingual Convolutional, Long Short-Term Memory, Deep Neural Networks for Low Resource Speech Recognition , 2017 .

[32]  Elad Hoffer,et al.  Train longer, generalize better: closing the generalization gap in large batch training of neural networks , 2017, NIPS.

[33]  William T. Freeman,et al.  Learning the Depths of Moving People by Watching Frozen People , 2019, 2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR).

[34]  Daniel Rueckert,et al.  Real-Time Single Image and Video Super-Resolution Using an Efficient Sub-Pixel Convolutional Neural Network , 2016, 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR).

[35]  P. Langley,et al.  Computational Models of Scientific Discovery and Theory Formation , 1990 .

[36]  Ronan Collobert,et al.  wav2vec: Unsupervised Pre-training for Speech Recognition , 2019, INTERSPEECH.

[37]  Aaron Klein,et al.  Efficient and Robust Automated Machine Learning , 2015, NIPS.

[38]  Hanlin Tang,et al.  Untangling in Invariant Speech Recognition , 2020, NeurIPS.

[39]  Lars Kotthoff,et al.  Automated Machine Learning: Methods, Systems, Challenges , 2019, The Springer Series on Challenges in Machine Learning.

[40]  J. Guttmann,et al.  Identifying Mathematical Models of the Mechanically Ventilated Lung Using Equation Discovery , 2009 .

[41]  Hugo Jair Escalante,et al.  Particle Swarm Model Selection for Authorship Verification , 2009, CIARP.

[42]  Fatih Murat Porikli,et al.  CDnet 2014: An Expanded Change Detection Benchmark Dataset , 2014, 2014 IEEE Conference on Computer Vision and Pattern Recognition Workshops.

[43]  Manuel Laguna,et al.  Tabu Search , 1997 .

[44]  Jan M. Zytkow,et al.  Interactive Mining of Regularities in Databases , 1991, Knowledge Discovery in Databases.

[45]  Marko Heikkilä,et al.  A texture-based method for modeling the background and detecting moving objects , 2006, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[46]  David J. Spiegelhalter,et al.  Machine Learning, Neural and Statistical Classification , 2009 .

[47]  Matti Pietikäinen,et al.  Multiresolution Gray-Scale and Rotation Invariant Texture Classification with Local Binary Patterns , 2002, IEEE Trans. Pattern Anal. Mach. Intell..

[48]  Michael N. Vrahatis,et al.  Particle Swarm Optimization and Intelligence: Advances and Applications , 2010 .

[49]  Luc Van Gool,et al.  The Pascal Visual Object Classes (VOC) Challenge , 2010, International Journal of Computer Vision.

[50]  Ljup Co Todorovski.  Declarative Bias in Equation Discovery , 1997 .

[51]  Yoshua Bengio,et al.  Generative Adversarial Nets , 2014, NIPS.

[52]  Stefan Roth,et al.  Covariance Matrix Adaptation for Multi-objective Optimization , 2007, Evolutionary Computation.

[53]  Pat Langley,et al.  Elements of Machine Learning , 1995 .

[54]  Saso Dzeroski,et al.  Integrating Domain Knowledge in Equation Discovery , 2007, Computational Discovery of Scientific Knowledge.

[55]  Brian Falkenhainer,et al.  Integrating quantitative and qualitative discovery: The ABACUS system , 2004, Machine Learning.

[56]  Isabelle Guyon,et al.  An Introduction to Variable and Feature Selection , 2003, J. Mach. Learn. Res..

[57]  Antoine Vacavant,et al.  A comprehensive review of background subtraction algorithms evaluated with synthetic and real videos , 2014, Comput. Vis. Image Underst..

[58]  Max Welling,et al.  Auto-Encoding Variational Bayes , 2013, ICLR.

[59]  Tali Dekel,et al.  SinGAN: Learning a Generative Model From a Single Natural Image , 2019, 2019 IEEE/CVF International Conference on Computer Vision (ICCV).

[60]  Quoc V. Le,et al.  Neural Architecture Search with Reinforcement Learning , 2016, ICLR.

[61]  Saso Dzeroski,et al.  Equation Discovery for Nonlinear System Identification , 2019, IEEE Access.

[62]  Guigang Zhang,et al.  Deep Learning , 2016, Int. J. Semantic Comput..

[63]  Juliana Freire,et al.  AlphaD3M: Machine Learning Pipeline Synthesis , 2021, ArXiv.

[64]  Jürgen Schmidhuber,et al.  Long Short-Term Memory , 1997, Neural Computation.

[65]  Jan M. Zytkow,et al.  Combining many searches in the FAHRENHEIT discovery system , 1987 .

[66]  Yoshua Bengio,et al.  Learning Phrase Representations using RNN Encoder–Decoder for Statistical Machine Translation , 2014, EMNLP.

[67]  Chen Liang,et al.  AutoML-Zero: Evolving Machine Learning Algorithms From Scratch , 2020, ICML.

[68]  Vlado Stankovski,et al.  An equation-discovery approach to earthquake-ground-motion prediction , 2013, Eng. Appl. Artif. Intell..

[69]  Hahn-Ming Lee,et al.  Model selection of SVMs using GA approach , 2004, 2004 IEEE International Joint Conference on Neural Networks (IEEE Cat. No.04CH37541).

[70]  Quoc V. Le,et al.  Sequence to Sequence Learning with Neural Networks , 2014, NIPS.