Tensor networks are a decomposition of high-dimensional tensors into multiple
smaller tensors. They were first introduced in quantum physics, and have been
adopted in machine learning in recent years. A special type of tensor network
is matrix product state (MPS), which is a chain-shaped tensor network. Its
expressiveness is limited by the bond dimension, which bounds the correlations
the model can represent.
In this thesis we use an MPS Born machine as a probabilistic model for
tabular data. In a single MPS model we can simultaneously use different
types of embeddings for different attributes (nominal, ordinal and continuous).
In contrast to most generative models, the MPS Born machine allows exact
likelihood evaluation, exact marginal and conditional distributions and can
efficiently implement ancestral sampling. The bond dimension is adapted to
the data during DMRG-style training.
We implement and evaluate the model on a categorical dataset about breast
cancer. We show that one-dimensional marginal distributions of synthetic
data match the real data and that the model is able to represent correlations
between pairs of attributes.
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