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Variational Inference with Continuously-Indexed Normalizing Flows [article]

Anthony Caterini and Rob Cornish and Dino Sejdinovic and Arnaud Doucet
2021 arXiv   pre-print
Continuously-indexed flows (CIFs) have recently achieved improvements over baseline normalizing flows on a variety of density estimation tasks.  ...  CIFs do not possess a closed-form marginal density, and so, unlike standard flows, cannot be plugged in directly to a variational inference (VI) scheme in order to produce a more expressive family of approximate  ...  Arnaud Doucet is supported by the EPSRC CoSInES (COmputational Statistical INference for Engineering and Security) grant EP/R034710/1  ... 
arXiv:2007.05426v2 fatcat:pik3fevfwvaglgbn6lbl5u4onu

Continuous Latent Process Flows [article]

Ruizhi Deng, Marcus A. Brubaker, Greg Mori, Andreas M. Lehrmann
2021 arXiv   pre-print
We tackle these challenges with continuous latent process flows (CLPF), a principled architecture decoding continuous latent processes into continuous observable processes using a time-dependent normalizing  ...  Fitting this type of data using statistical models with continuous dynamics is not only promising at an intuitive level but also has practical benefits, including the ability to generate continuous trajectories  ...  Continuous Indexing. More recently, normalizing flows have been augmented with a continuous index [7, 11, 12] .  ... 
arXiv:2106.15580v2 fatcat:p6b5f6wghjf7laqk4sjlhzg4xy

Fat-Tailed Variational Inference with Anisotropic Tail Adaptive Flows [article]

Feynman Liang, Liam Hodgkinson, Michael W. Mahoney
2022 arXiv   pre-print
While fat-tailed densities commonly arise as posterior and marginal distributions in robust models and scale mixtures, they present challenges when Gaussian-based variational inference fails to capture  ...  Experimental results on both synthetic and real-world targets confirm that ATAF is competitive with prior work while also exhibiting appropriate tail-anisotropy.  ...  ADVI (with normalizing flows) comprise the variational family Q ADVI := {(f • Φ Flow ) * µ} where µ = Normal(0 d , I d ), Φ Flow is an invertible flow transform (e.g., Table 1 ) and f is a deterministic  ... 
arXiv:2205.07918v1 fatcat:we7cimv4cffv7pzledsrmpewce

Bayesian Nonparametric Models for Multiway Data Analysis

Zenglin Xu, Feng Yan, Yuan Qi
2015 IEEE Transactions on Pattern Analysis and Machine Intelligence  
Tensor-variate Gaussian Process • Remarks: • TGP is equivalent to defining Tucker decomposition with infinite feature mapping , and an infinite core tensor ∞ • Each element of ∞ is a standard normal random  ...  ) and (Yan et al., 2011) Tensor-variate T Process Inference (Probit noise) • E-step (continued) • where • where , and . • and . • M-step • Maximize the expected log-likelihood: • After eliminating  ... 
doi:10.1109/tpami.2013.201 pmid:26353255 fatcat:gegbkpfthve5xl6wwo4o4fldta

Reliable Categorical Variational Inference with Mixture of Discrete Normalizing Flows [article]

Tomasz Kuśmierczyk, Arto Klami
2021 arXiv   pre-print
We provide an alternative differentiable reparameterization for categorical distribution by composing it as a mixture of discrete normalizing flows.  ...  Variational approximations are increasingly based on gradient-based optimization of expectations estimated by sampling.  ...  step with normalizing flows, and with Continuously Indexed Flows [Cornish et al., 2019] in challenging the bijection assumption.  ... 
arXiv:2006.15568v2 fatcat:delvtnvefrflno5tyt7bzpd2ei

Uncertainty Flow Facilitates Zero-Shot Multi-Label Learning in Affective Facial Analysis

Wenjun Bai, Changqin Quan, Zhiwei Luo
2018 Applied Sciences  
Featured Application: The proposed Uncertainty Flow framework may benefit the facial analysis with its promised elevation in discriminability in multi-label affective classification tasks.  ...  The success of our proposed Uncertainty Flow provides a glimpse of future in continuous, uncertain, and multi-label affective computing.  ...  Architecture: Same as ML-CNN Priors: Normal/Uniform/Cauchy Inference Method: Variational Mean Field Number of Posterior Sampling: 500.  ... 
doi:10.3390/app8020300 fatcat:q7nuexgum5aljbtb75yw26bxbe

Fault Detection in a Continuous Pulp Digester

Pascal Dufour, Sharad Bhartiya, Thomas J. English, Edward P. Gatzke, Prasad S. Dhurjati, Francis J. Doyle
2001 IFAC Proceedings Volumes  
The first one is concerned with the variations of the kappa number, i.e., the pulp quality index at the extraction of the digester vessel.  ...  The chips, however, continue their downward flow in the modified continuous cooking (MCC) zone and extended modified continuous cooking (EMCC) zone where they encounter weak liquor flowing countercurrently  ... 
doi:10.1016/s1474-6670(17)33574-7 fatcat:xrvoggb4w5bbdk2sjj37e5wt6i

Latent Normalizing Flows for Discrete Sequences [article]

Zachary M. Ziegler, Alexander M. Rush
2019 arXiv   pre-print
Normalizing flows are a powerful class of generative models for continuous random variables, showing both strong model flexibility and the potential for non-autoregressive generation.  ...  Our results indicate that an autoregressive flow-based model can match the performance of a comparable autoregressive baseline, and a non-autoregressive flow-based model can improve generation speed with  ...  Instead we explore using a latentvariable model, with a continuous latent sequence modeled through normalizing flows.  ... 
arXiv:1901.10548v4 fatcat:7g3dbgmck5hbfoitsguucn2yse

The equivalence between Stein variational gradient descent and black-box variational inference [article]

Casey Chu, Kentaro Minami, Kenji Fukumizu
2020 arXiv   pre-print
We formalize an equivalence between two popular methods for Bayesian inference: Stein variational gradient descent (SVGD) and black-box variational inference (BBVI).  ...  This work thereby unifies several existing techniques in variational inference and generative modeling and identifies the kernel as a fundamental object governing the behavior of these algorithms, motivating  ...  inference Black-box variational inference (Ranganath et al., 2014) , or BBVI, is another technique for Bayesian inference that approximates the true posterior p(x) with an approximate posterior q φ (  ... 
arXiv:2004.01822v1 fatcat:ibbzjdqkkbdcznoo4t6vwem7gy

Extensional Tectonics and Basement Uplift of the Fansipan and Tule Mountain Ranges in Northern Vietnam

Thi-Hue Dinh, Thi-Hue Dinh, Thi-Hue Dinh, Yu-Chang Chan, Yu-Chang Chan, Chih-Tung Chen
2022 Frontiers in Earth Science  
of the inferred normal faults and low values for the hanging walls.  ...  In addition to these observations, the results from geomorphic indices, which include both the stream-length gradient index (SL) and normalized steepness index (ksn), present high values for the footwalls  ...  Variations in lithology may affect the SL values when rivers flow across contacts with different rock types with different rock strengths (Hack, 1973) .  ... 
doi:10.3389/feart.2021.741670 doaj:34906d3ce6d34ddc82746fa957f28aea fatcat:xwvrdcczwbefjf3ii5abaa4aty

Task-agnostic Continual Learning with Hybrid Probabilistic Models [article]

Polina Kirichenko, Mehrdad Farajtabar, Dushyant Rao, Balaji Lakshminarayanan, Nir Levine, Ang Li, Huiyi Hu, Andrew Gordon Wilson, Razvan Pascanu
2021 arXiv   pre-print
In this work we propose HCL, a Hybrid generative-discriminative approach to Continual Learning for classification. We model the distribution of each task and each class with a normalizing flow.  ...  the normalizing flow model.  ...  data with normalizing flows.  ... 
arXiv:2106.12772v1 fatcat:md7l4fhxkfa7nc5og2daonwlja

Adaptive-network-based Fuzzy Inference (anfis) Modelling of Particle Image Velocimetry (piv) Measurements in Stirred Tank Reactors

Carlos Enrique Gomez Camacho, Leonardo Clemente, Giulia Moretti, Bernardo Ruggeri
2020 Chemical Engineering Transactions  
The fitness of the produced models was scored by means of the fuzzy Goodness Index (GI), which combines the correlation coefficient (R2), index of agreement (IA) and relative root mean square error (RRMSE  ...  The present work presents an innovative machine-learning modelling approach which uses the adaptive-network-based fuzzy inference system (ANFIS) on experimentally velocity fields data collected through  ...  : i) the coefficient of determination (R 2 ), ii) the index of agreement (IA) and iii) the normalized root mean square error (RRMSE), as well as a fuzzy-based lumped indicator, the Goodness Index (GI)  ... 
doi:10.3303/cet2079001 doaj:58d318cad5e64602b1a42fb2812811bd fatcat:i7wwirycbfhntoay46gqkonpl4

The walker circulation and atmospheric water vapour characteristics over the Pacific for two contrasting years

Mary Toshie Kayano, Vadlamudi Brahmananda Rao, Antonio Divino Moura
1989 International Journal of Climatology  
Further, the correlation coefficient between the SO index and water vapour variation showed significant values.  ...  In the top and bottom figures the monthly normals (long-term means) are shown as continuous and broken lines, respectively.  ...  the SO index.  ... 
doi:10.1002/joc.3370090303 fatcat:nhbo2gsg5fa6dn5nommlqghg2i

Modeling Continuous Stochastic Processes with Dynamic Normalizing Flows [article]

Ruizhi Deng, Bo Chang, Marcus A. Brubaker, Greg Mori, Andreas Lehrmann
2021 arXiv   pre-print
Furthermore, our continuous treatment provides a natural framework for irregular time series with an independent arrival process, including straightforward interpolation.  ...  In this work, we propose a novel type of normalizing flow driven by a differential deformation of the Wiener process.  ...  C.3 CTFP-RealNVP In this experiment, we replace the continuous normalizing flow in CTFP model with another popular choice of normalizing flow model, RealNVP [14] .  ... 
arXiv:2002.10516v4 fatcat:75xbi3uiuff35mp2tlqguriy6q

SurVAE Flows: Surjections to Bridge the Gap between VAEs and Flows [article]

Didrik Nielsen, Priyank Jaini, Emiel Hoogeboom, Ole Winther, Max Welling
2020 arXiv   pre-print
Normalizing flows and variational autoencoders are powerful generative models that can represent complicated density functions.  ...  SurVAE Flows bridge the gap between normalizing flows and VAEs with surjective transformations, wherein the transformations are deterministic in one direction -- thereby allowing exact likelihood computation  ...  Funding Disclosure This research was supported by the NVIDIA Corporation with the donation of TITAN X GPUs.  ... 
arXiv:2007.02731v2 fatcat:7cozym4jendrliu2jnppmpprzu
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