Zoltán Szabó's Home Page

Zoltán Szabó [on Bitbucket, mloss]

Random Fourier Signature Features:

Large-scale, GPU-accelerated signature kernel estimators.
The signature kernel is among the most powerful measures of similarities of sequences of arbitrary length, with strong theoretical grounding.

Nyström M-HSIC:

Consistent estimation of HSIC for ≥ 2 components using the Nyström method.
Applications:
- weather causal discovery,
- dependency testing of media annotations.

Kernelized Cumulants:

Higher-degree generalization of MMD and HSIC.
Applications:
- environmental and traffic data analysis,
- two-sample and independence testing.

Hard SDP Shape-Constrained Kernel Machines:

Kernel machines with hard affine SDP constraints on function values and function derivatives.
Applications:
- shape optimization (minimizing the deformation of a catenary under its weight, with a stand underneath),
- safety-critical control (piloting an underwater vehicle while avoiding obstacles),
- robotics (estimation of robotic arm position),
- econometrics (learning production functions).

Functional Output Regression with Infimal Convolution:

Vector-Valued Infinite Task Learning:

Hard Shape-Constrained Kernel Machines:

Kernel machines with hard affine shape constraints on function values and function derivatives.
Applications:
- joint quantile regression,
- economics,
- analysis of aircraft trajectories.

Outlier-Robust MMD Estimation:

Estimation of MMD (maximum mean discrepancy, a divergence measure on kernel-endowed domains) in the presence of outliers, using the median-of-means principle.
Applications:
- two-sample testing,
- gene analysis.

Infinite-Task Learning:

Generic approach to learn continuum number of tasks jointly via vector-valued RKHSs.
Applications:
- cost-sensitive classification,
- joint quantile regression,
- density level set estimation.

Adaptive Linear-Time Nonparametric Hypothesis Tests:

Two-sample tests:
- Adaptivity: features & kernel parameters are chosen to optimize power. The power of the tests matches quadratic-time tests. The returned features indicate why the two distributions differ.
- Applications:
  - NLP (distinguishing articles from two categories),
  - computer vision (differentiating positive and negative emotions).
Independence tests:
- Applications: dependency testing of media annotations:
  - song - year of release,
  - video - caption.
Goodness-of-fit tests:
- Best Paper Award @ NIPS-2017! (=top 0.09%)
- Application: analysis of criminal data.

Information Theoretical Estimators (ITE) Toolbox [in Python, Matlab]:

Several estimators for entropy, mutual information, divergence, association measures and kernels on probability distributions.
Applications:
- independent subspace analysis,
- outlier-robust image registration,
- distribution regression (aerosol prediction from multispectral satellite images).

KMC (Kernel Hamiltonian Monte Carlo):

A gradient-free adaptive MCMC algorithm based on Hamiltonian Monte Carlo (HMC). On target densities where classical HMC is not an option due to intractable gradients, KMC adaptively learns the target's gradient structure from the sample path, by fitting an exponential family model in a Reproducing Kernel Hilbert Space.
Applications:
- sampling from the marginal posterior of hyper-parameters in Gaussian process classification,
- approximate Bayesian computation.

LL-LVM (Locally Linear Latent Variable Model):

A probabilistic model for non-linear manifold discovery that describes a joint distribution over observations, their manifold coordinates and locally linear maps conditioned on a set of neighbourhood relationships; 'Bayesian LLE'.
Application: climate data analysis.

Kernel-EP (Kernel based just-in-time Expectation Propagation):

OSDL (Online Group-Structured Dictionary Learning) [rar/zip/tar]:

Structured-sparse dictionary learning method which (i) is online, (ii) allows overlapping group structures with (iii) non-convex group-structure inducing regularization, and (iv) handles incomplete observations.
Applications:
- collaborative filtering,
- image inpainting.