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Nishiyama Lab
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A lab that develops computational methods for machine learning, drawing on optimal transport and kernel methods.
AboutAbout the lab
Supporting machine learning with the mathematics of probability distributions.
The Nishiyama Lab studies the mathematics and algorithms of machine learning.
It works on optimal transport, which measures the difference between probability distributions, and on computational methods for Bayesian inference based on kernel methods.
Recent master's and bachelor's theses have addressed topics such as improvements to the Sinkhorn algorithm and machine learning using the Wasserstein distance.
Key terms
- optimal transport
- An approach that finds the minimum "cost of transport" needed to move one probability distribution to another. It is used to measure the difference between distributions.
- kernel Bayesian inference
- A method that maps data into a feature space (a reproducing kernel Hilbert space) and performs Bayesian inference there.
- state-space model
- A time-series model in which a hidden state changes over time and observed data are generated from that state.
ResearchResearch themes
Learning, inference, and prediction from the vast amounts of data around us, such as images, audio, and time series, depend on mathematical algorithms that support them. Building on the mathematics of probability distributions, such as optimal transport and kernel methods, this lab studies computational methods for machine learning.
Optimal Transport and the Sinkhorn Algorithm
The lab investigates computational techniques, such as low-rank approximation and sparsification, for the Sinkhorn algorithm, which is used to solve optimal transport problems quickly. It also works on extensions of the Sinkhorn divergence and on applications to unbalanced optimal transport problems.
Wasserstein Distance and Machine Learning
This research applies the Wasserstein distance, which is defined through optimal transport, to machine learning. Topics include its use in training variational autoencoders, optimization on Wasserstein space, and speeding up clustering using optimal transport.
Kernel Bayesian Inference and Time Series
Within the framework of kernel Bayesian inference, the lab has developed filtering and smoothing algorithms for state-space models. It has developed a filtering method that considers continuous-time models, and a fiscal 2023 master's thesis also covered improvements to the kernel Kalman filter.
MembersFaculty
The Nishiyama Lab consists of faculty members and master's and undergraduate students.As of 2026
- Associate ProfessorYu Nishiyama
VoicesStudent voices
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Report an errorAbout the images
The top and research theme images are illustrative and were not taken at the lab. They are cropped from Wikimedia Commons images. Cropped CC BY-SA images are provided under the same CC BY-SA license as the original (version shown on each line).
- Top image: “Piles of sand at the sand quarry - geograph.org.uk - 1592459” Christine Johnstone / CC BY-SA 2.0 (cropped)
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