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Gaussian process regression is widely used because of its ability to provide well-calibrated uncertainty estimates and handle small or sparse datasets. However, it struggles with high-dimensional data. One possible way to scale this…

We develop a framework for derivative Gaussian process latent variable models (DGP-LVMs) that can handle multi-dimensional output data using modified derivative covariance functions. The modifications account for complexities in the…

Open-domain semantic parsing remains a challenging task, as neural models often rely on heuristics and struggle to handle unseen concepts. In this paper, we investigate the potential of large language models (LLMs) for this task and…

In this paper, we propose a progressive learning paradigm for transformer-based variable-rate image compression. Our approach covers a wide range of compression rates with the assistance of the Layer-adaptive Prompt Module (LPM). Inspired…

Multimodal Large Language Models (MLLMs) have achieved notable gains in various tasks by incorporating Chain-of-Thought (CoT) reasoning in language spaces. Recent work extends this direction by leveraging external tools for visual editing,…

We introduce a variational Bayesian neural network where the parameters are governed via a probability distribution on random matrices. Specifically, we employ a matrix variate Gaussian \cite{gupta1999matrix} parameter posterior…

Humans continue to outperform modern AI systems in their ability to flexibly parse and understand complex visual scenes. Here, we present a novel module for visual reasoning, the Guided Attention Model for (visual) Reasoning (GAMR), which…

Recent empirical evidence shows that LLM representations encode human-interpretable concepts. Nevertheless, the mechanisms by which these representations emerge remain largely unexplored. To shed further light on this, we introduce a novel…

Bayesian methods have become a popular way to incorporate prior knowledge and a notion of uncertainty into machine learning models. At the same time, the complexity of modern machine learning makes it challenging to comprehend a model's…

We consider the problem of covariance matrix estimation in the presence of latent variables. Under suitable conditions, it is possible to learn the marginal covariance matrix of the observed variables via a tractable convex program, where…

We consider the estimation of an i.i.d.\ random vector observed through a linear transform followed by a componentwise, probabilistic (possibly nonlinear) measurement channel. A novel algorithm, called generalized approximate message…

Bayesian learning using Gaussian processes provides a foundational framework for making decisions in a manner that balances what is known with what could be learned by gathering data. In this dissertation, we develop techniques for…

Gaussian processes (GPs) have gained popularity as flexible machine learning models for regression and function approximation with an in-built method for uncertainty quantification. However, GPs suffer when the amount of training data is…

Gaussian processes allow for flexible specification of prior assumptions of unknown dynamics in state space models. We present a procedure for efficient Bayesian learning in Gaussian process state space models, where the representation is…

Graph representation learning is a fundamental problem for modeling relational data and benefits a number of downstream applications. Traditional Bayesian-based graph models and recent deep learning based GNN either suffer from…

Understanding, predicting, and generating object motions and transformations is a core problem in artificial intelligence. Modeling sequences of evolving images may provide better representations and models of motion and may ultimately be…

Complex-valued signals are used in the modeling of many systems in engineering and science, hence being of fundamental interest. Often, random complex-valued signals are considered to be proper. A proper complex random variable or process…

We consider the abstract relational reasoning task, which is commonly used as an intelligence test. Since some patterns have spatial rationales, while others are only semantic, we propose a multi-scale architecture that processes each query…

We present LatentAM, an online 3D Gaussian Splatting (3DGS) mapping framework that builds scalable latent feature maps from streaming RGB-D observations for open-vocabulary robotic perception. Instead of distilling high-dimensional…

Humans can approach complex visual problems by mentally simulating intermediate visual steps, rather than reasoning through language alone. Inspired by this, several works on Vision-Language Models have recently explored chain-of-thought…