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Paper · 2312.08200 · 2023

SPD-DDPM: Denoising Diffusion Probabilistic Models in the Symmetric Positive Definite Space

arXiv · PDF · Open in the Atlas

Code that ran

We lifted 13 functions out of this paper's own repositories and ran 11 of them in a sandbox. "Ran" means the function executed on a synthesized input and returned a value. It is not a reproduction of the paper's results.

RepositoryRoleRan
li-yun-chen/spd-ddpm canonical 11 of 13
FunctionStatusWhere it lives
adjust_learning_rate Ran li-yun-chen/spd-ddpm/condition/ddpm.py
pointer only (licence: NONE) · get_code("1c854ffce06dbac4")
betas_for_alpha_bar Ran li-yun-chen/spd-ddpm/uncondition/ddpm.py
pointer only (licence: NONE) · get_code("d07c1a93d2fa327d")
fro Ran li-yun-chen/spd-ddpm/exp2/conditional_dis.py
pointer only (licence: NONE) · get_code("5ba4fbd489d1601f")
generate_init Ran li-yun-chen/spd-ddpm/uncondition/generate_train_sample_setting1.py
pointer only (licence: NONE) · get_code("d5dd04635d4e6f5e")
remove_subtensors_with_nan Ran li-yun-chen/spd-ddpm/uncondition/ddpm.py
pointer only (licence: NONE) · get_code("ceb7b714828f151f")
row_to_matrix Ran li-yun-chen/spd-ddpm/exp1/heatplot.py
pointer only (licence: NONE) · get_code("2c79ca7b063199ab")
select_rows_from_csv Ran li-yun-chen/spd-ddpm/exp1/heatplot.py
pointer only (licence: NONE) · get_code("dccfa3edebee5d5b")
spd_dis Ran li-yun-chen/spd-ddpm/condition/support_function.py
pointer only (licence: NONE) · get_code("a4413dcb7b30cc69")
spd_minus Ran li-yun-chen/spd-ddpm/condition/support_function.py
pointer only (licence: NONE) · get_code("ccfceecb8fd4787a")
spd_plus Ran li-yun-chen/spd-ddpm/condition/support_function.py
pointer only (licence: NONE) · get_code("52011d088aa4ca91")
tensor_power Ran li-yun-chen/spd-ddpm/exp2/conditional_dis.py
pointer only (licence: NONE) · get_code("0578b08a27d3103e")
one_param Not yet run li-yun-chen/spd-ddpm/condition/SPD_net.py
pointer only (licence: NONE) · get_code("4b602b0867bad430")
symmetric Not yet run li-yun-chen/spd-ddpm/condition/SPD_net.py
pointer only (licence: NONE) · get_code("e9b42bb505335112")

Repositories linked to this paper

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Abstract

Symmetric positive definite~(SPD) matrices have shown important value and applications in statistics and machine learning, such as FMRI analysis and traffic prediction. Previous works on SPD matrices mostly focus on discriminative models, where predictions are made directly on $E(X|y)$, where $y$ is a vector and $X$ is an SPD matrix. However, these methods are challenging to handle for large-scale data, as they need to access and process the whole data. In this paper, inspired by denoising diffusion probabilistic model~(DDPM), we propose a novel generative model, termed SPD-DDPM, by introducing Gaussian distribution in the SPD space to estimate $E(X|y)$. Moreover, our model is able to estimate $p(X)$ unconditionally and flexibly without giving $y$. On the one hand, the model conditionally learns $p(X|y)$ and utilizes the mean of samples to obtain $E(X|y)$ as a prediction. On the other hand, the model unconditionally learns the probability distribution of the data $p(X)$ and generates samples that conform to this distribution. Furthermore, we propose a new SPD net which is much deeper than the previous networks and allows for the inclusion of conditional factors. Experiment results on toy data and real taxi data demonstrate that our models effectively fit the data distribution both unconditionally and unconditionally and provide accurate predictions.

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