arXiv subjects

Sinead A. Williamson

Publications and source records attributed to Sinead A. Williamson.

At least 19 recordsLinked to original sources

arXiv2026

Detecting State Changes in Functional Neuronal Connectivity using Factorial Switching Linear Dynamical Systems

A key question in brain sciences is how to identify time-evolving functional connectivity, such as that obtained from recordings of neuronal activity over time. We wish to explain the observed phenomena in terms of latent states which, in the case of neuronal activity, might correspond to subnetworks of neurons within a brain or organoid. Many existing approaches assume that only one latent state can be active at a time, in contrast to our domain knowledge. We propose a switching dynamical system based on the factorial hidden Markov model. Unlike existing approaches, our model acknowledges that neuronal activity can be caused by multiple subnetworks, which may be activated either jointly or independently. A change in one part of the network does not mean that the entire connectivity pattern will change. We pair our model with scalable variational inference algorithm, using a concrete relaxation of the underlying factorial hidden Markov model, to effectively infer the latent states and model parameters. We show that our algorithm can recover ground-truth structure and yield insights about the maturation of neuronal activity in microelectrode array recordings from in vitro neuronal cultures.

stat.ME↗

arXiv2023

Sequential Gaussian Processes for Online Learning of Nonstationary Functions

Many machine learning problems can be framed in the context of estimating functions, and often these are time-dependent functions that are estimated in real-time as observations arrive. Gaussian processes (GPs) are an attractive choice for modeling real-valued nonlinear functions due to their flexibility and uncertainty quantification. However, the typical GP regression model suffers from several drawbacks: 1) Conventional GP inference scales $O(N^{3})$ with respect to the number of observations; 2) Updating a GP model sequentially is not trivial; and 3) Covariance kernels typically enforce stationarity constraints on the function, while GPs with non-stationary covariance kernels are often intractable to use in practice. To overcome these issues, we propose a sequential Monte Carlo algorithm to fit infinite mixtures of GPs that capture non-stationary behavior while allowing for online, distributed inference. Our approach empirically improves performance over state-of-the-art methods for online GP estimation in the presence of non-stationarity in time-series data. To demonstrate the utility of our proposed online Gaussian process mixture-of-experts approach in applied settings, we show that we can sucessfully implement an optimization algorithm using online Gaussian process bandits.

stat.ML↗

arXiv2022

Denoising neural networks for magnetic resonance spectroscopy

In many scientific applications, measured time series are corrupted by noise or distortions. Traditional denoising techniques often fail to recover the signal of interest, particularly when the signal-to-noise ratio is low or when certain assumptions on the signal and noise are violated. In this work, we demonstrate that deep learning-based denoising methods can outperform traditional techniques while exhibiting greater robustness to variation in noise and signal characteristics. Our motivating example is magnetic resonance spectroscopy, in which a primary goal is to detect the presence of short-duration, low-amplitude radio frequency signals that are often obscured by strong interference that can be difficult to separate from the signal using traditional methods. We explore various deep learning architecture choices to capture the inherently complex-valued nature of magnetic resonance signals. On both synthetic and experimental data, we show that our deep learning-based approaches can exceed performance of traditional techniques, providing a powerful new class of methods for analysis of scientific time series data.

cs.LG↗

arXiv2022

Accelerated Parallel Non-conjugate Sampling for Bayesian Non-parametric Models

Inference of latent feature models in the Bayesian nonparametric setting is generally difficult, especially in high dimensional settings, because it usually requires proposing features from some prior distribution. In special cases, where the integration is tractable, we can sample new feature assignments according to a predictive likelihood. We present a novel method to accelerate the mixing of latent variable model inference by proposing feature locations based on the data, as opposed to the prior. First, we introduce an accelerated feature proposal mechanism that we show is a valid MCMC algorithm for posterior inference. Next, we propose an approximate inference strategy to perform accelerated inference in parallel. A two-stage algorithm that combines the two approaches provides a computationally attractive method that can quickly reach local convergence to the posterior distribution of our model, while allowing us to exploit parallelization.

stat.ML↗

arXiv2021

Understanding collections of related datasets using dependent MMD coresets

Understanding how two datasets differ can help us determine whether one dataset under-represents certain sub-populations, and provides insights into how well models will generalize across datasets. Representative points selected by a maximum mean discrepency (MMD) coreset can provide interpretable summaries of a single dataset, but are not easily compared across datasets. In this paper we introduce dependent MMD coresets, a data summarization method for collections of datasets that facilitates comparison of distributions. We show that dependent MMD coresets are useful for understanding multiple related datasets and understanding model generalization between such datasets.

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arXiv2021

Balance is key: Private median splits yield high-utility random trees

Random forests are a popular method for classification and regression due to their versatility. However, this flexibility can come at the cost of user privacy, since training random forests requires multiple data queries, often on small, identifiable subsets of the training data. Privatizing these queries typically comes at a high utility cost, in large part because we are privatizing queries on small subsets of the data, which are easily corrupted by added noise. In this paper, we propose DiPriMe forests, a novel tree-based ensemble method for differentially private regression and classification, which is appropriate for real or categorical covariates. We generate splits using a differentially private version of the median, which encourages balanced leaf nodes. By avoiding low occupancy leaf nodes, we avoid high signal-to-noise ratios when privatizing the leaf node sufficient statistics. We show theoretically and empirically that the resulting algorithm exhibits high utility, while ensuring differential privacy.

cs.LG↗

arXiv2020

Importance Weighted Generative Networks

Deep generative networks can simulate from a complex target distribution, by minimizing a loss with respect to samples from that distribution. However, often we do not have direct access to our target distribution - our data may be subject to sample selection bias, or may be from a different but related distribution. We present methods based on importance weighting that can estimate the loss with respect to a target distribution, even if we cannot access that distribution directly, in a variety of settings. These estimators, which differentially weight the contribution of data to the loss function, offer both theoretical guarantees and impressive empirical performance.

stat.ML↗

arXiv2020

A Nonparametric Bayesian Model for Sparse Dynamic Multigraphs

As the availability and importance of temporal interaction data--such as email communication--increases, it becomes increasingly important to understand the underlying structure that underpins these interactions. Often these interactions form a multigraph, where we might have multiple interactions between two entities. Such multigraphs tend to be sparse yet structured, and their distribution often evolves over time. Existing statistical models with interpretable parameters can capture some, but not all, of these properties. We propose a dynamic nonparametric model for interaction multigraphs that combines the sparsity of edge-exchangeable multigraphs with dynamic clustering patterns that tend to reinforce recent behavioral patterns. We show that our method yields improved held-out likelihood over stationary variants, and impressive predictive performance against a range of state-of-the-art dynamic graph models.

cs.LG↗

arXiv2020

Distributed, partially collapsed MCMC for Bayesian Nonparametrics

Bayesian nonparametric (BNP) models provide elegant methods for discovering underlying latent features within a data set, but inference in such models can be slow. We exploit the fact that completely random measures, which commonly used models like the Dirichlet process and the beta-Bernoulli process can be expressed as, are decomposable into independent sub-measures. We use this decomposition to partition the latent measure into a finite measure containing only instantiated components, and an infinite measure containing all other components. We then select different inference algorithms for the two components: uncollapsed samplers mix well on the finite measure, while collapsed samplers mix well on the infinite, sparsely occupied tail. The resulting hybrid algorithm can be applied to a wide class of models, and can be easily distributed to allow scalable inference without sacrificing asymptotic convergence guarantees.

stat.ML↗

arXiv2020

Embarrassingly Parallel Inference for Gaussian Processes

Training Gaussian process-based models typically involves an $ O(N^3)$ computational bottleneck due to inverting the covariance matrix. Popular methods for overcoming this matrix inversion problem cannot adequately model all types of latent functions, and are often not parallelizable. However, judicious choice of model structure can ameliorate this problem. A mixture-of-experts model that uses a mixture of $K$ Gaussian processes offers modeling flexibility and opportunities for scalable inference. Our embarrassingly parallel algorithm combines low-dimensional matrix inversions with importance sampling to yield a flexible, scalable mixture-of-experts model that offers comparable performance to Gaussian process regression at a much lower computational cost.

stat.ML↗

arXiv2019

Sequential Edge Clustering in Temporal Multigraphs

Interaction graphs, such as those recording emails between individuals or transactions between institutions, tend to be sparse yet structured, and often grow in an unbounded manner. Such behavior can be well-captured by structured, nonparametric edge-exchangeable graphs. However, such exchangeable models necessarily ignore temporal dynamics in the network. We propose a dynamic nonparametric model for interaction graphs that combine the sparsity of the exchangeable models with dynamic clustering patterns that tend to reinforce recent behavioral patterns. We show that our method yields improved held-out likelihood over stationary variants, and impressive predictive performance against a range of state-of-the-art dynamic interaction graph models.

cs.LG↗

arXiv2019

Avoiding Resentment Via Monotonic Fairness

Classifiers that achieve demographic balance by explicitly using protected attributes such as race or gender are often politically or culturally controversial due to their lack of individual fairness, i.e. individuals with similar qualifications will receive different outcomes. Individually and group fair decision criteria can produce counter-intuitive results, e.g. that the optimal constrained boundary may reject intuitively better candidates due to demographic imbalance in similar candidates. Both approaches can be seen as introducing individual resentment, where some individuals would have received a better outcome if they either belonged to a different demographic class and had the same qualifications, or if they remained in the same class but had objectively worse qualifications (e.g. lower test scores). We show that both forms of resentment can be avoided by using monotonically constrained machine learning models to create individually fair, demographically balanced classifiers.

stat.ML↗

arXiv2019

Random clique covers for graphs with local density and global sparsity

Large real-world graphs tend to be sparse, but they often contain many densely connected subgraphs and exhibit high clustering coefficients. While recent random graph models can capture this sparsity, they ignore the local density, or vice versa. We develop a Bayesian nonparametric graph model based on random edge clique covers, and show that this model can capture power law degree distribution, global sparsity and non-vanishing local clustering coefficient. This distribution can be used directly as a prior on observed graphs, or as part of a hierarchical Bayesian model for inferring latent graph structures.

stat.ME↗

arXiv2019

A New Class of Time Dependent Latent Factor Models with Applications

In many applications, observed data are influenced by some combination of latent causes. For example, suppose sensors are placed inside a building to record responses such as temperature, humidity, power consumption and noise levels. These random, observed responses are typically affected by many unobserved, latent factors (or features) within the building such as the number of individuals, the turning on and off of electrical devices, power surges, etc. These latent factors are usually present for a contiguous period of time before disappearing; further, multiple factors could be present at a time. This paper develops new probabilistic methodology and inference methods for random object generation influenced by latent features exhibiting temporal persistence. Every datum is associated with subsets of a potentially infinite number of hidden, persistent features that account for temporal dynamics in an observation. The ensuing class of dynamic models constructed by adapting the Indian Buffet Process --- a probability measure on the space of random, unbounded binary matrices --- finds use in a variety of applications arising in operations, signal processing, biomedicine, marketing, image analysis, etc. Illustrations using synthetic and real data are provided.

stat.ML↗

arXiv2019

Stochastic Blockmodels with Edge Information

Stochastic blockmodels allow us to represent networks in terms of a latent community structure, often yielding intuitions about the underlying social structure. Typically, this structure is inferred based only on a binary network representing the presence or absence of interactions between nodes, which limits the amount of information that can be extracted from the data. In practice, many interaction networks contain much more information about the relationship between two nodes. For example, in an email network, the volume of communication between two users and the content of that communication can give us information about both the strength and the nature of their relationship. In this paper, we propose the Topic Blockmodel, a stochastic blockmodel that uses a count-based topic model to capture the interaction modalities within and between latent communities. By explicitly incorporating information sent between nodes in our network representation, we are able to address questions of interest in real-world situations, such as predicting recipients for an email message or inferring the content of an unopened email. Further, by considering topics associated with a pair of communities, we are better able to interpret the nature of each community and the manner in which it interacts with other communities.

cs.SI↗

arXiv2019

Large-scale Collaborative Filtering with Product Embeddings

The application of machine learning techniques to large-scale personalized recommendation problems is a challenging task. Such systems must make sense of enormous amounts of implicit feedback in order to understand user preferences across numerous product categories. This paper presents a deep learning based solution to this problem within the collaborative filtering with implicit feedback framework. Our approach combines neural attention mechanisms, which allow for context dependent weighting of past behavioral signals, with representation learning techniques to produce models which obtain extremely high coverage, can easily incorporate new information as it becomes available, and are computationally efficient. Offline experiments demonstrate significant performance improvements when compared to several alternative methods from the literature. Results from an online setting show that the approach compares favorably with current production techniques used to produce personalized product recommendations.

cs.IR↗

arXiv2017

Parallel Markov Chain Monte Carlo for the Indian Buffet Process

Indian Buffet Process based models are an elegant way for discovering underlying features within a data set, but inference in such models can be slow. Inferring underlying features using Markov chain Monte Carlo either relies on an uncollapsed representation, which leads to poor mixing, or on a collapsed representation, which leads to a quadratic increase in computational complexity. Existing attempts at distributing inference have introduced additional approximation within the inference procedure. In this paper we present a novel algorithm to perform asymptotically exact parallel Markov chain Monte Carlo inference for Indian Buffet Process models. We take advantage of the fact that the features are conditionally independent under the beta-Bernoulli process. Because of this conditional independence, we can partition the features into two parts: one part containing only the finitely many instantiated features and the other part containing the infinite tail of uninstantiated features. For the finite partition, parallel inference is simple given the instantiation of features. But for the infinite tail, performing uncollapsed MCMC leads to poor mixing and hence we collapse out the features. The resulting hybrid sampler, while being parallel, produces samples asymptotically from the true posterior.

stat.ML↗

arXiv2015

Restricted Indian Buffet Processes

Latent feature models are a powerful tool for modeling data with globally-shared features. Nonparametric exchangeable models such as the Indian Buffet Process offer modeling flexibility by letting the number of latent features be unbounded. However, current models impose implicit distributions over the number of latent features per data point, and these implicit distributions may not match our knowledge about the data. In this paper, we demonstrate how the Restricted Indian Buffet Process circumvents this restriction, allowing arbitrary distributions over the number of features in an observation. We discuss several alternative constructions of the model and use the insights gained to develop Markov Chain Monte Carlo and variational methods for simulation and posterior inference.

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