Taehee Lee

Taehee Lee, Jun S. Liu

Despite the widespread utilization of Gaussian process models for versatile nonparametric modeling, they exhibit limitations in effectively capturing abrupt changes in function smoothness and accommodating relationships with heteroscedastic errors. Addressing these shortcomings, the heteroscedastic Gaussian process (HeGP) regression seeks to introduce flexibility by acknowledging the variability of residual variances across covariates in the regression model. In this work, we extend the HeGP concept, expanding its scope beyond regression tasks to encompass classification and state-space models. To achieve this, we propose a novel framework where the Gaussian process is coupled with a covariate-induced precision matrix process, adopting a mixture formulation. This approach enables the modeling of heteroscedastic covariance functions across covariates. To mitigate the computational challenges posed by sampling, we employ variational inference to approximate the posterior and facilitate posterior predictive modeling. Additionally, our training process leverages an EM algorithm featuring closed-form M-step updates to efficiently evaluate the heteroscedastic covariance function. A notable feature of our model is its consistent performance on multivariate responses, accommodating various types (continuous or categorical) seamlessly. Through a combination of simulations and real-world applications in climatology, we illustrate the model's prowess and advantages. By overcoming the limitations of traditional Gaussian process models, our proposed framework offers a robust and versatile tool for a wide array of applications.

JoonHo Lee, Jae Oh Woo, Juree Seok et al.

Assessing response quality to instructions in language models is vital but challenging due to the complexity of human language across different contexts. This complexity often results in ambiguous or inconsistent interpretations, making accurate assessment difficult. To address this issue, we propose a novel Uncertainty-aware Reward Model (URM) that introduces a robust uncertainty estimation for the quality of paired responses based on Bayesian approximation. Trained with preference datasets, our uncertainty-enabled proxy not only scores rewards for responses but also evaluates their inherent uncertainty. Empirical results demonstrate significant benefits of incorporating the proposed proxy into language model training. Our method boosts the instruction following capability of language models by refining data curation for training and improving policy optimization objectives, thereby surpassing existing methods by a large margin on benchmarks such as Vicuna and MT-bench. These findings highlight that our proposed approach substantially advances language model training and paves a new way of harnessing uncertainty within language models.

Taehee Lee, Charles E. Lawrence

To restore the historical sea surface temperatures (SSTs) better, it is important to construct a good calibration model for the associated proxies. In this paper, we introduce a new model for alkenone (${\rm{U}}_{37}^{\rm{K}'}$) based on the heteroscedastic Gaussian process (GP) regression method. Our nonparametric approach not only deals with the variable pattern of noises over SSTs but also contains a Bayesian method of classifying potential outliers.

Taehee Lee, Lorraine E. Lisiecki, Devin Rand et al.

We first introduce a novel profile-based alignment algorithm, the multiple continuous Signal Alignment algorithm with Gaussian Process Regression profiles (SA-GPR). SA-GPR addresses the limitations of currently available signal alignment methods by adopting a hybrid of the particle smoothing and Markov-chain Monte Carlo (MCMC) algorithms to align signals, and by applying the Gaussian process regression to construct profiles to be aligned continuously. SA-GPR shares all the strengths of the existing alignment algorithms that depend on profiles but is more exact in the sense that profiles do not need to be discretized as sequential bins. The uncertainty of performance over the resolution of such bins is thereby eliminated. This methodology produces alignments that are consistent, that regularize extreme cases, and that properly reflect the inherent uncertainty. Then we extend SA-GPR to a specific problem in the field of paleoceanography with a method called Bayesian Inference Gaussian Process Multiproxy Alignment of Continuous Signals (BIGMACS). The goal of BIGMACS is to infer continuous ages for ocean sediment cores using two classes of age proxies: proxies that explicitly return calendar ages (e.g., radiocarbon) and those used to synchronize ages in multiple marine records (e.g., an oxygen isotope based marine proxy known as benthic $δ^{18}{\rm O}$). BIGMACS integrates these two proxies by iteratively performing two steps: profile construction from benthic $δ^{18}{\rm O}$ age models and alignment of each core to the profile also reflecting radiocarbon dates. We use BIGMACS to construct a new Deep Northeastern Atlantic stack (i.e., a profile from a particular benthic $δ^{18}{\rm O}$ records) of five ocean sediment cores. We conclude by constructing multiproxy age models for two additional cores from the same region by aligning them to the stack.