Related papers: Unifying Probabilistic Models for Time-Frequency A…
Approximate Bayesian inference methods that scale to very large datasets are crucial in leveraging probabilistic models for real-world time series. Sparse Markovian Gaussian processes combine the use of inducing variables with efficient…
A two space dimensional active nonlinear nonlocal cochlear model is formulated in the time domain to capture nonlinear hearing effects such as compression, multi-tone suppression and difference tones. The micromechanics of the basilar…
Kalman filtering and smoothing are the foundational mechanisms for efficient inference in Gauss-Markov models. However, their time and memory complexities scale prohibitively with the size of the state space. This is particularly…
Analyzing time series in the frequency domain enables the development of powerful tools for investigating the second-order characteristics of multivariate processes. Parameters like the spectral density matrix and its inverse, the coherence…
The Gaussian Process Convolution Model (GPCM; Tobar et al., 2015a) is a model for signals with complex spectral structure. A significant limitation of the GPCM is that it assumes a rapidly decaying spectrum: it can only model smooth…
State-space models are used in a wide range of time series analysis formulations. Kalman filtering and smoothing are work-horse algorithms in these settings. While classic algorithms assume Gaussian errors to simplify estimation, recent…
Gaussian processes are ubiquitous in machine learning, statistics, and applied mathematics. They provide a flexible modelling framework for approximating functions, whilst simultaneously quantifying uncertainty. However, this is only true…
Gaussian process regression is a frequently used statistical method for flexible yet fully probabilistic non-linear regression modeling. A common obstacle is its computational complexity which scales poorly with the number of observations.…
The Dynamical Gaussian Process Latent Variable Models provide an elegant non-parametric framework for learning the low dimensional representations of the high-dimensional time-series. Real world observational studies, however, are often…
Beam search with masked language models (MLMs) is challenging in part because joint probability distributions over sequences are not readily available, unlike for autoregressive models. However, estimating such distributions has important…
The Gaussian process state-space model (GPSSM) has garnered considerable attention over the past decade. However, the standard GP with a preliminary kernel, such as the squared exponential kernel or Mat\'{e}rn kernel, that is commonly used…
State-space models can be used to incorporate subject knowledge on the underlying dynamics of a time series by the introduction of a latent Markov state-process. A user can specify the dynamics of this process together with how the state…
Gaussian process (GP) audio source separation is a time-domain approach that circumvents the inherent phase approximation issue of spectrogram based methods. Furthermore, through its kernel, GPs elegantly incorporate prior knowledge about…
We present a deep generative model for unsupervised text style transfer that unifies previously proposed non-generative techniques. Our probabilistic approach models non-parallel data from two domains as a partially observed parallel…
Probabilistic programming has emerged as a powerful paradigm in statistics, applied science, and machine learning: by decoupling modelling from inference, it promises to allow modellers to directly reason about the processes generating…
The problem of incorporating information from observations received serially in time is widespread in the field of uncertainty quantification. Within a probabilistic framework, such problems can be addressed using standard filtering…
Probabilistic modeling is fundamental to the statistical analysis of complex data. In addition to forming a coherent description of the data-generating process, probabilistic models enable parameter inference about given data sets. This…
The outcome statistics of an informationally complete quantum measurement for a system in a given state can be used to evaluate the ensemble expectation of any linear operator in the same state, by averaging a function of the outcomes that…
A probabilistic machine learning model is introduced to augment the $k-\omega\ SST$ turbulence model in order to improve the modelling of separated flows and the generalisability of learnt corrections. Increasingly, machine learning methods…
Climate change poses significant challenges for accurate climate modeling due to the complexity and variability of non-Gaussian climate systems. To address the complexities of non-Gaussian systems in climate modeling, this thesis proposes a…