Active multi-fidelity Bayesian online changepoint detection

Online algorithms for detecting changepoints, or abrupt shifts in the behavior of a time series, are often deployed with limited resources, e.g., to edge computing settings such as mobile phones or industrial sensors. In these scenarios it may be beneficial to trade the cost of collecting an environmental measurement against the quality or "fidelity" of this measurement and how the measurement affects changepoint estimation. For instance, one might decide between inertial measurements or GPS to determine changepoints for motion. A Bayesian approach to changepoint detection is particularly appealing because we can represent our posterior uncertainty about changepoints and make active, cost-sensitive decisions about data fidelity to reduce this posterior uncertainty. Moreover, the total cost could be dramatically lowered through active fidelity switching, while remaining robust to changes in data distribution. We propose a multi-fidelity approach that makes cost-sensitive decisions about which data fidelity to collect based on maximizing information gain with respect to changepoints. We evaluate this framework on synthetic, video, and audio data and show that this information-based approach results in accurate predictions while reducing total cost.Comment: 37th Conference on Uncertainty in Artificial Intelligenc

Adaptation of the Tuning Parameter in General Bayesian Inference with Robust Divergence

We introduce a methodology for robust Bayesian estimation with robust divergence (e.g., density power divergence or {\gamma}-divergence), indexed by a single tuning parameter. It is well known that the posterior density induced by robust divergence gives highly robust estimators against outliers if the tuning parameter is appropriately and carefully chosen. In a Bayesian framework, one way to find the optimal tuning parameter would be using evidence (marginal likelihood). However, we numerically illustrate that evidence induced by the density power divergence does not work to select the optimal tuning parameter since robust divergence is not regarded as a statistical model. To overcome the problems, we treat the exponential of robust divergence as an unnormalized statistical model, and we estimate the tuning parameter via minimizing the Hyvarinen score. We also provide adaptive computational methods based on sequential Monte Carlo (SMC) samplers, which enables us to obtain the optimal tuning parameter and samples from posterior distributions simultaneously. The empirical performance of the proposed method through simulations and an application to real data are also provided

Bayesian Non-parametric Hidden Markov Model for Agile Radar Pulse Sequences Streaming Analysis

Multi-function radars (MFRs) are sophisticated types of sensors with the capabilities of complex agile inter-pulse modulation implementation and dynamic work mode scheduling. The developments in MFRs pose great challenges to modern electronic reconnaissance systems or radar warning receivers for recognition and inference of MFR work modes. To address this issue, this paper proposes an online processing framework for parameter estimation and change point detection of MFR work modes. At first, this paper designed a fully-conjugate Bayesian non-parametric hidden Markov model with a designed prior distribution (agile BNP-HMM) to represent the MFR pulse agility characteristics. The proposed model allows fully-variational Bayesian inference. Then, the proposed framework is constructed by two main parts. The first part is the agile BNP-HMM model for automatically inferring the number of HMM hidden states and emission distribution of the corresponding hidden states. An estimation error lower bound on performance is derived and the proposed algorithm is shown to be close to the bound. The second part utilizes the streaming Bayesian updating to facilitate computation, and designed an online work mode change detection framework based upon a weighted sequential probability ratio test. We demonstrate that the proposed framework is consistently highly effective and robust to baseline methods on diverse simulated data-sets.Comment: 15 pages, 10 figures, submitted to IEEE transactions on signal processin

Robust and Scalable Bayesian Online Changepoint Detection

This paper proposes an online, provably robust, and scalable Bayesian approach for changepoint detection. The resulting algorithm has key advantages over previous work: it provides provable robustness by leveraging the generalised Bayesian perspective, and also addresses the scalability issues of previous attempts. Specifically, the proposed generalised Bayesian formalism leads to conjugate posteriors whose parameters are available in closed form by leveraging diffusion score matching. The resulting algorithm is exact, can be updated through simple algebra, and is more than 10 times faster than its closest competitor

Differentially Private Statistical Inference through β\beta-Divergence One Posterior Sampling

Differential privacy guarantees allow the results of a statistical analysis involving sensitive data to be released without compromising the privacy of any individual taking part. Achieving such guarantees generally requires the injection of noise, either directly into parameter estimates or into the estimation process. Instead of artificially introducing perturbations, sampling from Bayesian posterior distributions has been shown to be a special case of the exponential mechanism, producing consistent, and efficient private estimates without altering the data generative process. The application of current approaches has, however, been limited by their strong bounding assumptions which do not hold for basic models, such as simple linear regressors. To ameliorate this, we propose $\beta$D-Bayes, a posterior sampling scheme from a generalised posterior targeting the minimisation of the $\beta$-divergence between the model and the data generating process. This provides private estimation that is generally applicable without requiring changes to the underlying model and consistently learns the data generating parameter. We show that $\beta$D-Bayes produces more precise inference estimation for the same privacy guarantees, and further facilitates differentially private estimation via posterior sampling for complex classifiers and continuous regression models such as neural networks for the first time

Generalised Bayesian filtering via sequential Monte Carlo

We introduce a framework for inference in general state-space hidden Markov models (HMMs) under likelihood misspecification. In particular, we leverage the loss-theoretic perspective of Generalized Bayesian Inference (GBI) to define generalised filtering recursions in HMMs, that can tackle the problem of inference under model misspecification. In doing so, we arrive at principled procedures for robust inference against observation contamination by utilising the $\beta$-divergence. Operationalising the proposed framework is made possible via sequential Monte Carlo methods (SMC), where the standard particle methods, and their associated convergence results, are readily adapted to the new setting. We demonstrate our approach to object tracking and Gaussian process regression problems, and observe improved performance over standard filtering algorithms