Bayes

Background Bayesian neural networks is a principled technique to learn the function that maps input to output, while quantifying the uncertainty of the problem. Due to the computational complexity exact inference is prohibited and among several approaches Laplace approximation is a rather simple but yet effective way for approximate inference [1]. Recently, a geometric extension relying on Riemannian manifolds has been proposed that enables Laplace approximation to adapt to the local structure of the posterior [2]. This new Riemannian Laplace approximation is effective and meaningful, but it comes with an increase to the computational cost. In this project, we will consider techniques to: 1) improve the computational efficiency of the Riemannian Laplace approximation, and 2) provide a relaxation of the basic approach that is potentially fast while retaining the geometric characteristics. ...

Background The Laplace approximation is a promising approach to posterior approximation which can address some core issues of deep learning such as poor calibration. Scaling this method to large parameters spaces is intractable because the covariance matrix is quadratic in the number of neural network parameters and hence cannot be stored in memory. A proposed solution to this problem is to only treat a subset of the parameters as stochastic [1, 2, 3] and treat the rest as deterministic. However the method of selecting a subnetwork is still an open problem. In this project we will explore the possibility of learning optimal subnetwork structure by instantiating the small covariance matrix and backpropogating through a Bayesian loss function (ELBO, Marginal Likelihood, Predictive Posterior Distribution). ...

Background This project will develop arithmetic’s for Probabilistic Tensor Train Decomposition (Hinrich & Mørup, 2019) and apply it to solving large-scale linear problems which are relevant for a variety of applications, e.g. in quantum computing/physics, machine learning, and finance. First, consider the linear problem, A x = b, where A, x, and b are an N by M matrix, M by 1 vector, and N by 1 vector, respectively. In large-scale linear problems M and N are large numbers that have exponential scaling, e.g. $M=m^d$ and $N=n^d$ for some m,n < 10, but d in the tens or hundreds which leads to exponential computational and storage complexity for conventional methods. ...

Background Variational Auto-Encoders (VAEs) are useful models for learning non-linear latent representations of data. Usually, VAEs are learned by obtaining an approximation of the maximum likelihood estimate of the parameters through the evidence lower bound. In VAEs Bayesian Variational Auto-Encoders (B-VAEs), we obtain, instead, a posterior distribution of the parameters, leading to a more robust model, e.g., for out of distribution detection (Daxberger and Hernández-Lobato, 2019). Bayesian VAEs are typically trained by learning a variational posterior approximation of both the latent variable and the model parameters. ...

Background A multimodal model is any model that takes in one or more different modalities of data. This could be text and images, image and audio ect. An example of this is the CLIP model [1], that learns embeddings of text and images simultaneously. Common methods for explainability in general focus on a single modality e.g. what part of an image was important for a given prediction. The purpose of this project is to investigate how methods for single modality explainability can be extended to multimodality data. ...

Background When designing and training machine learning architectures for medical data, we often neglect prior knowledge about the data domain. In this project, we want to investigate whether we can find shared information between medical signals and their corresponding textual descriptions. Current advances in the field of NLP have made it possible to learn rich contextual information from textual data. Given cross-modality observations, Relative Representations make it possible to compare and align latent spaces of different modalities or models. ...

Background Data augmentation is used to increase the diversity of a dataset by applying various transformations to the existing data, which helps improve model generalization, performance, and robustness while reducing the risk of overfitting. For this project, you will begin by surveying existing methods and metrics. Afterwards, you will focus on creating new methods for learning a data augmentation scheme in order to optimize one or more selected metrics. You will evaluate your methods using well-established benchmark datasets in a selected data domain and task, which could be images, time series, or molecular graph data, e.g. for classification. Objective(s) i) Survey the state of the art in data augmentation, and compare > performance on several metrics such as generalization with respect > to performance, robustness to covariate shift, and uncertainty > quantification. ...

Background Speech enhancement is the task of recovering clean speech from noisy speech that has been degraded due to e.g. background noise, interfering speakers or reverberation in poor acoustic conditions. Deep learning-based speech enhancement is typically trained in a supervised setup using datasets consisting of separate clean speech and background noise samples, which are combined at training time and the network is then trained to directly recover the clean speech from the artificially corrupted mixture. This artificial mixing step limits the diversity of data that models are exposed to and harms the resulting models’ ability to generalize. ...

Background Speech enhancement is the task of recovering clean speech from noisy speech that has been degraded due to e.g. background noise, interfering speakers or reverberation in poor acoustic conditions. Deep learning-based speech enhancement is typically trained in a supervised setup using datasets consisting of separate clean speech and background noise samples, which are combined at training time and the network is then trained to directly recover the clean speech from the artificially corrupted mixture. This artificial mixing step limits the diversity of data that models are exposed to and harms the resulting model’s ability to generalize to real-world conditions. ...