Clustered Federated Learning (CFL) improves performance under non-IID client heterogeneity by clustering clients and training one model per cluster, thereby balancing between a global model and fully personalized models. However, most CFL methods require the number of clusters K to be fixed a priori, which is impractical when the latent structure is unknown. We propose DPMM-CFL, a CFL algorithm that places a Dirichlet Process (DP) prior over the distribution of cluster parameters. This enables nonparametric Bayesian inference to jointly infer both the number of clusters and client assignments, while optimizing per-cluster federated objectives. This results in a method where, at each round, federated updates and cluster inferences are coupled, as presented in this paper. The algorithm is validated on benchmark datasets under Dirichlet and class-split non-IID partitions.

We develop a sequential low-complexity inference procedure for Dirichlet process mixtures of Gaussians for online clustering and parameter estimation when the number of clusters are unknown a-priori. We present an easily computable, closed form parametric expression for the conditional likelihood, in which hyper-parameters are recursively updated as a function of the streaming data assuming conjugate priors. Motivated by large-sample asymptotics, we propose a novel adaptive low-complexity design for the Dirichlet process concentration parameter and show that the number of classes grow at most at a logarithmic rate. We further prove that in the large-sample limit, the conditional likelihood and data predictive distribution become asymptotically Gaussian. We demonstrate through experiments on synthetic and real data sets that our approach is superior to other online state-of-the-art methods.

Variational inference algorithms provide the most effective framework for large-scale training of Bayesian nonparametric models. Stochastic online approaches are promising, but are sensitive to the chosen learning rate and often converge to poor local optima. We present a new algorithm, memoized online variational inference, which scales to very large (yet finite) datasets while avoiding the complexities of stochastic gradient. Our algorithm maintains finite-dimensional sufficient statistics from batches of the full dataset, requiring some additional memory but still scaling to millions of examples. Exploiting nested families of variational bounds for infinite nonparametric models, we develop principled birth and merge moves allowing non-local optimization.

We develop a sequential low-complexity inference procedure for Dirichlet process mixtures of Gaussians for online clustering and parameter estimation when the number of clusters are unknown a-priori. We present an easily computable, closed form parametric expression for the conditional likelihood, in which hyperparameters are recursively updated as a function of the streaming data assuming conjugate priors. Motivated by large-sample asymptotics, we propose a noveladaptive low-complexity design for the Dirichlet process concentration parameter and show that the number of classes grow at most at a logarithmic rate. We further prove that in the large-sample limit, the conditional likelihood and datapredictive distribution become asymptotically Gaussian. We demonstrate through experiments on synthetic and real data sets that our approach is superior to otheronline state-of-the-art methods.

Based on audio recordings made once a month during the first 12 months of a child's life, we propose a new method for clustering this set of vocalizations. We use a topologically augmented representation of the vocalizations, employing two persistence diagrams for each vocalization: one computed on the surface of its spectrogram and one on the Takens' embeddings of the vocalization. A synthetic persistent variable is derived for each diagram and added to the MFCCs (Mel-frequency cepstral coefficients). Using this representation, we fit a non-parametric Bayesian mixture model with a Dirichlet process prior to model the number of components. This procedure leads to a novel data-driven categorization of vocal productions. Our findings reveal the presence of 8 clusters of vocalizations, allowing us to compare their temporal distribution and acoustic profiles in the first 12 months of life.

Skill discovery algorithms in reinforcement learning typically identify single states or regions in state space that correspond to task-specific subgoals. However, such methods do not directly address the question of how many distinct skills are appropriate for solving the tasks that the agent faces. This can be highly inefficient when many identified subgoals correspond to the same underlying skill, but are all used individually as skill goals. Furthermore, skills created in this manner are often only transferable to tasks that share identical state spaces, since corresponding subgoals across tasks are not merged into a single skill goal. We show that these problems can be overcome by clustering subgoal data defined in an agent-space and using the resulting clusters as templates for skill termination conditions. Clustering via a Dirichlet process mixture model is used to discover a minimal, sufficient collection of portable skills.

We present a nonparametric Bayesian approach to inverse reinforcement learning (IRL) for multiple reward functions. Most previous IRL algorithms assume that the behaviour data is obtained from an agent who is optimizing a single reward function, but this assumption is hard to guarantee in practice. Our approach is based on integrating the Dirichlet process mixture model into Bayesian IRL. We provide an efficient Metropolis-Hastings sampling algorithm utilizing the gradient of the posterior to estimate the underlying reward functions, and demonstrate that our approach outperforms previous ones via experiments on a number of problem domains.

Variational inference algorithms provide the most effective framework for largescale training of Bayesian nonparametric models. Stochastic online approaches are promising, but are sensitive to the chosen learning rate and often converge to poor local optima. We present a new algorithm, memoized online variational inference, which scales to very large (yet finite) datasets while avoiding the complexities of stochastic gradient. Our algorithm maintains finite-dimensional sufficient statistics from batches of the full dataset, requiring some additional memory but still scaling to millions of examples. Exploiting nested families of variational bounds for infinite nonparametric models, we develop principled birth and merge moves allowing non-local optimization. Births adaptively add components to the model to escape local optima, while merges remove redundancy and improve speed. Using Dirichlet process mixture models for image clustering and denoising, we demonstrate major improvements in robustness and accuracy.