We consider the problem of online learning in the presence of distribution shifts that occur at an unknown rate and of unknown intensity. We derive a new Bayesian online inference approach to simultaneously infer these distribution shifts and adapt the model to the detected changes by integrating ideas from change point detection, switching dynamical systems, and Bayesian online learning. Using a binary'change variable,' we construct an informative prior such that-if a change is detected-the model partially erases the information of past model updates by tempering to facilitate adaptation to the new data distribution. Furthermore, the approach uses beam search to track multiple change-point hypotheses and selects the most probable one in hindsight. Our proposed method is model-agnostic, applicable in both supervised and unsupervised learning settings, suitable for an environment of concept drifts or covariate drifts, and yields improvements over state-of-the-art Bayesian online learning approaches.

In unsupervised causal representation learning for sequential data with time-delayed latent causal influences, strong identifiability results for the disentanglement of causally-related latent variables have been established in stationary settings by leveraging temporal structure. However, in nonstationary setting, existing work only partially addressed the problem by either utilizing observed auxiliary variables (e.g., class labels and/or domain indexes) as side-information or assuming simplified latent causal dynamics. Both constrain the method to a limited range of scenarios. In this study, we further explored the Markov Assumption under time-delayed causally related process in nonstationary setting and showed that under mild conditions, the independent latent components can be recovered from their nonlinear mixture up to a permutation and a component-wise transformation, without the observation of auxiliary variables. We then introduce NCTRL, a principled estimation framework, to reconstruct time-delayed latent causal variables and identify their relations from measured sequential data only. Empirical evaluations demonstrated the reliable identification of time-delayed latent causal influences, with our methodology substantially outperforming existing baselines that fail to exploit the nonstationarity adequately and then, consequently, cannot distinguish distribution shifts.

We study a class of classification problems best exemplified by the bank loan problem, where a lender decides whether or not to issue a loan. The lender only observes whether a customer will repay a loan if the loan is issued to begin with, and thus modeled decisions affect what data is available to the lender for future decisions. As a result, it is possible for the lender's algorithm to "get stuck" with a self-fulfilling model. This model never corrects its false negatives, since it never sees the true label for rejected data, thus accumulating infinite regret. In the case of linear models, this issue can be addressed by adding optimism directly into the model predictions. However, there are few methods that extend to the function approximation case using Deep Neural Networks.

We study the problem of properly learning linear threshold functions (LTFs) in the learning from label proportions (LLP) framework. In this, the learning is on a collection of bags of feature-vectors with only the proportion of labels available for each bag. First, we provide an algorithm that, given a collection of such bags each of size at most two whose label proportions are consistent with (i.e., the bags are satisfied by) an unknown LTF, efficiently produces an LTF that satisfies at least (2/5)-fraction of the bags. If all the bags are non-monochromatic (i.e., bags of size two with differently labeled feature-vectors) the algorithm satisfies at least (1/2)-fraction of them. For the special case of OR over the d-dimensional boolean vectors, we give an algorithm which computes an LTF achieving an additional Ω(1/d) in accuracy for the two cases.

Conventional supervised learning methods, especially deep ones, are found to be sensitive to out-of-distribution (OOD) examples, largely because the learned representation mixes the semantic factor with the variation factor due to their domain-specific correlation, while only the semantic factor causes the output. To address the problem, we propose a Causal Semantic Generative model (CSG) based on a causal reasoning so that the two factors are modeled separately, and develop methods for OOD prediction from a single training domain, which is common and challenging. The methods are based on the causal invariance principle, with a novel design in variational Bayes for both efficient learning and easy prediction. Theoretically, we prove that under certain conditions, CSG can identify the semantic factor by fitting training data, and this semantic-identification guarantees the boundedness of OOD generalization error and the success of adaptation. Empirical study shows improved OOD performance over prevailing baselines.