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Kaspar Märtens

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Statistical machine learning, probabilistic inference, deep generative models, Gaussian Processes

Kaspar is a DPhil student at the Department of Statistics, University of Oxford, supervised by Christopher Yau and Chris Holmes.

He has a broad interest in statistical machine learning and Bayesian inference techniques, with a focus on tackling real problems in genomics and healthcare. His PhD research focuses on developing probabilistic latent variable models (such as Gaussian Process Latent Variable Models and Variational Autoencoders) with applications to biomedical data.

Kaspar is also an R enthusiast and organises the Oxford R user group meetings.

Publications

2020

• K. Märtens , C. Yau , BasisVAE: Translation-invariant feature-level clustering with Variational Autoencoders, International Conference on Artificial Intelligence and Statistics (AISTATS), 2020.
  
  Variational Autoencoders (VAEs) provide a flexible and scalable framework for non-linear dimensionality reduction. However, in application domains such as genomics where data sets are typically tabular and high-dimensional, a black-box approach to dimensionality reduction does not provide sufficient insights. Common data analysis workflows additionally use clustering techniques to identify groups of similar features. This usually leads to a two-stage process, however, it would be desirable to construct a joint modelling framework for simultaneous dimensionality reduction and clustering of features. In this paper, we propose to achieve this through the BasisVAE: a combination of the VAE and a probabilistic clustering prior, which lets us learn a one-hot basis function representation as part of the decoder network. Furthermore, for scenarios where not all features are aligned, we develop an extension to handle translation-invariant basis functions. We show how a collapsed variational inference scheme leads to scalable and efficient inference for BasisVAE, demonstrated on various toy examples as well as on single-cell gene expression data.

  @article{martens2020basisVAE,
    title = {{BasisVAE}: {Translation}-invariant feature-level clustering with {Variational} {Autoencoders}},
    journal = {International Conference on Artificial Intelligence and Statistics (AISTATS)},
    author = {Märtens, Kaspar and Yau, Christopher},
    year = {2020}
  }
  

• K. Märtens , C. Yau , Neural Decomposition: Functional ANOVA with Variational Autoencoders, International Conference on Artificial Intelligence and Statistics (AISTATS), 2020.
  
  Variational Autoencoders (VAEs) have become a popular approach for dimensionality reduction. However, despite their ability to identify latent low-dimensional structures embedded within high-dimensional data, these latent representations are typically hard to interpret on their own. Due to the black-box nature of VAEs, their utility for healthcare and genomics applications has been limited. In this paper, we focus on characterising the sources of variation in Conditional VAEs. Our goal is to provide a feature-level variance decomposition, i.e. to decompose variation in the data by separating out the marginal additive effects of latent variables z and fixed inputs c from their non-linear interactions. We propose to achieve this through what we call Neural Decomposition – an adaptation of the well-known concept of functional ANOVA variance decomposition from classical statistics to deep learning models. We show how identifiability can be achieved by training models subject to constraints on the marginal properties of the decoder networks. We demonstrate the utility of our Neural Decomposition on a series of synthetic examples as well as high-dimensional genomics data.

  @article{martens2020neural,
    title = {Neural {Decomposition}: {Functional} {ANOVA} with {Variational} {Autoencoders}},
    journal = {International Conference on Artificial Intelligence and Statistics (AISTATS)},
    author = {Märtens, Kaspar and Yau, Christopher},
    year = {2020}
  }
  

2019

• K. Märtens , K. Campbell , C. Yau , Decomposing feature-level variation with Covariate Gaussian Process Latent Variable Models, in Proceedings of the 36th International Conference on Machine Learning (ICML), 2019, vol. 97, 4372–4381.
  
  The interpretation of complex high-dimensional data typically requires the use of dimensionality reduction techniques to extract explanatory low-dimensional representations. However, in many real-world problems these representations may not be sufficient to aid interpretation on their own, and it would be desirable to interpret the model in terms of the original features themselves. Our goal is to characterise how feature-level variation depends on latent low-dimensional representations, external covariates, and non-linear interactions between the two. In this paper, we propose to achieve this through a structured kernel decomposition in a hybrid Gaussian Process model which we call the Covariate Gaussian Process Latent Variable Model (c-GPLVM). We demonstrate the utility of our model on simulated examples and applications in disease progression modelling from high-dimensional gene expression data in the presence of additional phenotypes. In each setting we show how the c-GPLVM can extract low-dimensional structures from high-dimensional data sets whilst allowing a breakdown of feature-level variability that is not present in other commonly used dimensionality reduction approaches.

  @inproceedings{pmlr-v97-martens19a,
    title = {Decomposing feature-level variation with Covariate Gaussian Process Latent Variable Models},
    author = {Märtens, Kaspar and Campbell, Kieran and Yau, Christopher},
    booktitle = {Proceedings of the 36th International Conference on Machine Learning (ICML)},
    pages = {4372--4381},
    year = {2019},
    editor = {Chaudhuri, Kamalika and Salakhutdinov, Ruslan},
    volume = {97},
    series = {Proceedings of Machine Learning Research},
    month = {09--15 Jun},
    publisher = {PMLR}
  }
  

• K. Märtens , M. Titsias , C. Yau , Augmented Ensemble MCMC sampling in Factorial Hidden Markov Models, in International Conference on Artificial Intelligence and Statistics (AISTATS), 2019, vol. 89, 2359–2367.
  
  Bayesian inference for Factorial Hidden Markov Models is challenging due to the exponentially sized latent variable space. Standard Monte Carlo samplers can have difficulties effectively exploring the posterior landscape and are often restricted to exploration around localised regions that depend on initialisation. We introduce a general purpose ensemble Markov Chain Monte Carlo (MCMC) technique to improve on existing poorly mixing samplers. This is achieved by combining parallel tempering and an auxiliary variable scheme to exchange information between the chains in an efficient way. The latter exploits a genetic algorithm within an augmented Gibbs sampler. We compare our technique with various existing samplers in a simulation study as well as in a cancer genomics application, demonstrating the improvements obtained by our augmented ensemble approach.

  @inproceedings{pmlr-v89-martens19a,
    title = {Augmented Ensemble MCMC sampling in Factorial Hidden Markov Models},
    author = {Märtens, Kaspar and Titsias, Michalis and Yau, Christopher},
    booktitle = {International Conference on Artificial Intelligence and Statistics (AISTATS)},
    pages = {2359--2367},
    year = {2019},
    editor = {Chaudhuri, Kamalika and Sugiyama, Masashi},
    volume = {89},
    series = {Proceedings of Machine Learning Research},
    address = {},
    month = {16--18 Apr},
    publisher = {PMLR}
  }
  

2016

• K. Märtens , J. Hallin , J. Warringer , G. Liti , L. Parts , Predicting quantitative traits from genome and phenome with near perfect accuracy, Nature Communications, vol. 7, 11512, 2016.
  

  @article{martens2016predicting,
    title = {Predicting quantitative traits from genome and phenome with near perfect accuracy},
    author = {Märtens, Kaspar and Hallin, Johan and Warringer, Jonas and Liti, Gianni and Parts, Leopold},
    journal = {Nature Communications},
    volume = {7},
    pages = {11512},
    year = {2016},
    publisher = {Nature Publishing Group}
  }
  

• J. Hallin , K. Märtens , A. I. Young , M. Zackrisson , F. Salinas , L. Parts , J. Warringer , G. Liti , Powerful decomposition of complex traits in a diploid model, Nature Communications, vol. 7, 13311, 2016.
  

  @article{hallin2016powerful,
    title = {Powerful decomposition of complex traits in a diploid model},
    author = {Hallin, Johan and Märtens, Kaspar and Young, Alexander I and Zackrisson, Martin and Salinas, Francisco and Parts, Leopold and Warringer, Jonas and Liti, Gianni},
    journal = {Nature Communications},
    volume = {7},
    pages = {13311},
    year = {2016},
    publisher = {Nature Publishing Group}
  }
  

• R. Kolde , K. Märtens , K. Lokk , S. Laur , J. Vilo , seqlm: an MDL based method for identifying differentially methylated regions in high density methylation array data, Bioinformatics, vol. 32, no. 17, 2604–2610, 2016.
  

  @article{kolde2016seqlm,
    title = {seqlm: an MDL based method for identifying differentially methylated regions in high density methylation array data},
    author = {Kolde, Raivo and Märtens, Kaspar and Lokk, Kaie and Laur, Sven and Vilo, Jaak},
    journal = {Bioinformatics},
    volume = {32},
    number = {17},
    pages = {2604--2610},
    year = {2016},
    publisher = {Oxford University Press}
  }
  

2014

• K. Lokk , V. Modhukur , B. Rajashekar , K. Märtens , R. Mägi , R. Kolde , M. Koltšina , T. K. Nilsson , J. Vilo , A. Salumets , . others , DNA methylome profiling of human tissues identifies global and tissue-specific methylation patterns, Genome Biology, vol. 15, no. 4, 3248, 2014.
  

  @article{lokk2014dna,
    title = {DNA methylome profiling of human tissues identifies global and tissue-specific methylation patterns},
    author = {Lokk, Kaie and Modhukur, Vijayachitra and Rajashekar, Balaji and Märtens, Kaspar and Mägi, Reedik and Kolde, Raivo and Kolt{\v{s}}ina, Marina and Nilsson, Torbj{\"o}rn K and Vilo, Jaak and Salumets, Andres and others},
    journal = {Genome Biology},
    volume = {15},
    number = {4},
    pages = {3248},
    year = {2014},
    publisher = {BioMed Central}
  }