Flat Posterior Does Matter For Bayesian Transfer Learning

The large-scale pre-trained neural network has achieved notable success in enhancing performance for downstream tasks. Another promising approach for generalization is Bayesian Neural Network (BNN), which integrates Bayesian methods into neural network architectures, offering advantages such as Bayesian Model averaging (BMA) and uncertainty quantification. Despite these benefits, transfer learning for BNNs has not been widely investigated and shows limited improvement. We hypothesize that this issue arises from the inability to find flat minima, which is crucial for generalization performance. To address this, we evaluate the sharpness of BNNs in various settings, revealing their insufficiency in seeking flat minima and the influence of flatness on BMA performance. Therefore, we propose Sharpness-aware Bayesian Model Averaging (SA-BMA), a Bayesian-fitting flat posterior seeking optimizer integrated with Bayesian transfer learning. SA-BMA calculates the divergence between posteriors in the parameter space, aligning with the nature of BNNs, and serves as a generalized version of existing sharpness-aware optimizers. We validate that SA-BMA improves generalization performance in few-shot classification and distribution shift scenarios by ensuring flatness.

Approximate Inference for Spectral Mixture Kernel

A spectral mixture (SM) kernel is a flexible kernel used to model any stationary covariance function. Although it is useful in modeling data, the learning of the SM kernel is generally difficult because optimizing a large number of parameters for the SM kernel typically induces an over-fitting, particularly when a gradient-based optimization is used. Also, a longer training time is required. To improve the training, we propose an approximate Bayesian inference for the SM kernel. Specifically, we employ the variational distribution of the spectral points to approximate SM kernel with a random Fourier feature. We optimize the variational parameters by applying a sampling-based variational inference to the derived evidence lower bound (ELBO) estimator constructed from the approximate kernel. To improve the inference, we further propose two additional strategies: (1) a sampling strategy of spectral points to estimate the ELBO estimator reliably and thus its associated gradient, and (2) an approximate natural gradient to accelerate the convergence of the parameters. The proposed inference combined with two strategies accelerates the convergence of the parameters and leads to better optimal parameters.

Implicit Kernel Attention

Attention compute the dependency between representations, and it encourages the model to focus on the important selective features. Among the attention methods, the scaled dot-product attention is widely utilized in many models. This paper suggests a generalized structure of the scaled dot-product attention with similarity and magnitude terms. We derive that the scaled dot-product attention is a product of two parts: 1) the RBF kernel to measure the similarity of two instances and 2) the exponential $L^{2}$ norm to compute the importance of individual instances. From this decomposition, we improve the attention in two ways: implicit modeling on the kernel spectral density and generalized $L^{p}$ norm, which results in a learnable and flexible attention structure. First, we estimate the spectral density of kernel with implicit probabilistic models to estimate the appropriate kernel for a given dataset without kernel selection manually. Second, we introduce a generalized $L^p$ norm on the hidden feature space, where $p$ is a hyper-parameter that affects the scale of individual importance and the sparsity of attention weights. Also, we show how to expand this implicit kernel modeling to multi-head attention in conjunction with a copula augmentation. Our generalized attention shows better performance on text classification, translation, regression, and node classification tasks.

Scalable Hybrid HMM with Gaussian Process Emission for Sequential Time-series Data Clustering

Hidden Markov Model (HMM) combined with Gaussian Process (GP) emission can be effectively used to estimate the hidden state with a sequence of complex input-output relational observations. Especially when the spectral mixture (SM) kernel is used for GP emission, we call this model as a hybrid HMM-GPSM. This model can effectively model the sequence of time-series data. However, because of a large number of parameters for the SM kernel, this model can not effectively be trained with a large volume of data having (1) long sequence for state transition and 2) a large number of time-series dataset in each sequence. This paper proposes a scalable learning method for HMM-GPSM. To effectively train the model with a long sequence, the proposed method employs a Stochastic Variational Inference (SVI) approach. Also, to effectively process a large number of data point each time-series data, we approximate the SM kernel using Reparametrized Random Fourier Feature (R-RFF). The combination of these two techniques significantly reduces the training time. We validate the proposed learning method in terms of its hidden-sate estimation accuracy and computation time using large-scale synthetic and real data sets with missing values.