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- Alexander Ilin, Tapani Raiko
- Journal of Machine Learning Research
- 2010

Principal component analysis (PCA) is a classical data analysis technique that finds linear transformations of data that retain the maximal amount of variance. We study a case where some of the data values are missing, and show that this problem has many features which are usually associated with nonlinear models, such as overfitting and bad locally optimal… (More)

- Tapani Raiko, Alexander Ilin, Juha Karhunen
- ECML
- 2007

Principal component analysis (PCA) is a well-known classical data analysis technique. There are a number of algorithms for solving the problem, some scaling better than others to problems with high dimensionality. They also differ in their ability to handle missing values in the data. We study a case where the data are high-dimensional and a majority of the… (More)

- Kyunghyun Cho, Tapani Raiko, Alexander Ilin
- Neural Computation
- 2013

Restricted Boltzmann machines (RBMs) are often used as building blocks in greedy learning of deep networks. However, training this simple model can be laborious. Traditional learning algorithms often converge only with the right choice of metaparameters that specify, for example, learning rate scheduling and the scale of the initial weights. They are also… (More)

- Kyunghyun Cho, Alexander Ilin, Tapani Raiko
- ICANN
- 2011

We propose a few remedies to improve training of Gaussian-Bernoulli restricted Boltzmann machines (GBRBM), which is known to be difficult. Firstly, we use a different parameterization of the energy function, which allows for more intuitive interpretation of the parameters and facilitates learning. Secondly, we propose parallel tempering learning for GBRBM.… (More)

Blind separation of sources from their linear mixtures is a well understood problem. However, if the mixtures are nonlinear, this problem becomes generally very difficult. This is because both the nonlinear mapping and the underlying sources must be learned from the data in a blind manner, and the problem is highly ill-posed without a suitable… (More)

- Jaakko Luttinen, Alexander Ilin
- NIPS
- 2009

We present a probabilistic factor analysis model which can be used for studying spatio-temporal datasets. The spatial and temporal structure is modeled by using Gaussian process priors both for the loading matrix and the factors. The posterior distributions are approximated using the variational Bayesian framework. High computational cost of Gaussian… (More)

- Alexander Ilin, Harri Valpola
- Neural Processing Letters
- 2005

We show that the choice of posterior approximation affects the solution found in Bayesian variational learning of linear independent component analysis models. Assuming the sources to be independent a posteriori favours a solution which has orthogonal mixing vectors. Linear mixing models with either temporally correlated sources or non-Gaussian source… (More)

- Kyunghyun Cho, Tapani Raiko, Alexander Ilin
- The 2010 International Joint Conference on Neural…
- 2010

A new interest towards restricted Boltzmann machines (RBMs) has risen due to their usefulness in greedy learning of deep neural networks. While contrastive divergence learning has been considered an efficient way to learn an RBM, it has a drawback due to a biased approximation in the learning gradient. We propose to use an advanced Monte Carlo method called… (More)

- Kyunghyun Cho, Tapani Raiko, Alexander Ilin
- ICML
- 2011

Boltzmann machines are often used as building blocks in greedy learning of deep networks. However, training even a simplified model, known as restricted Boltzmann machine (RBM), can be extremely laborious: Traditional learning algorithms often converge only with the right choice of the learning rate scheduling and the scale of the initial weights. They are… (More)

- Kyunghyun Cho, Tapani Raiko, Alexander Ilin
- The 2013 International Joint Conference on Neural…
- 2013

In this paper, we study a model that we call Gaussian-Bernoulli deep Boltzmann machine (GDBM) and discuss potential improvements in training the model. GDBM is designed to be applicable to continuous data and it is constructed from Gaussian-Bernoulli restricted Boltzmann machine (GRBM) by adding multiple layers of binary hidden neurons. The studied… (More)