In unsupervised domain adaptation, existing theory focuses on situations where the source and target domains are close. In practice, conditional entropy minimization and pseudo-labeling work even when the domain shifts are much larger than those analyzed by existing theory. We identify and analyze one particular setting where the domain shift can be large, but these algorithms provably work: certain spurious features correlate with the label in the source domain but are independent of the label in the target. Our analysis considers linear classification where the spurious features are Gaussian and the non-spurious features are a mixture of log-concave distributions. For this setting, we prove that entropy minimization on unlabeled target data will avoid using the spurious feature if initialized with a decently accurate source classifier, even though the objective is non-convex and contains multiple bad local minima using the spurious features. We verify our theory for spurious domain shift tasks on semi-synthetic Celeb-A and MNIST datasets. Our results suggest that practitioners collect and self-train on large, diverse datasets to reduce biases in classifiers even if labeling is impractical.

In real-world machine learning applications, even well-curated training datasets have various types of heterogeneity. Two main types of heterogeneity are: (1) data imbalance: the input or label distribution often has a long-tailed density, and (2) heteroskedasticity: the labels given inputs have varying levels of uncertainties across subsets of data stemming from various sources such as the intrinsic ambiguity of the data or annotation errors. Many deep learning algorithms have been proposed for imbalanced datasets (e.g., see [Wang et al., 2017, Cao et al., 2019, Cui et al., 2019, Liu et al., 2019] and the reference therein). However, heteroskedasticity, a classical notion studied extensively in the statistical community [Pintore et al., 2006, Wang et al., 2013, Tibshirani et al., 2014], has so far been under-explored in deep learning. This paper focuses on addressing heteroskedasticity and its interaction with data imbalance in deep learning. Heteroskedasticity is often studied in regression analysis and refers to the property that the distribution of the error varies across inputs. In this work, we mostly focus on classification, though the developed technique also applies to regression. Here, heteroskedasticity reflects how the uncertainty in the conditional distribution p(y x), or the entropy of y x, varies as a function of x .

Online machine learning systems need to adapt to domain shifts. Meanwhile, acquiring label at every timestep is expensive. We propose a surprisingly simple algorithm that adaptively balances its regret and its number of label queries in settings where the data streams are from a mixture of hidden domains. For online linear regression with oblivious adversaries, we provide a tight tradeoff that depends on the durations and dimensionalities of the hidden domains. Our algorithm can adaptively deal with interleaving spans of inputs from different domains. We also generalize our results to non-linear regression for hypothesis classes with bounded eluder dimension and adaptive adversaries. Experiments on synthetic and realistic datasets demonstrate that our algorithm achieves lower regret than uniform queries and greedy queries with equal labeling budget.

Exploration of the high-dimensional state action space is one of the biggest challenges in Reinforcement Learning (RL), especially in multi-agent domain. We present a novel technique called Experience Augmentation, which enables a time-efficient and boosted learning based on a fast, fair and thorough exploration to the environment. It can be combined with arbitrary off-policy MARL algorithms and is applicable to either homogeneous or heterogeneous environments. We demonstrate our approach by combining it with MADDPG and verifing the performance in two homogeneous and one heterogeneous environments. In the best performing scenario, the MADDPG with experience augmentation reaches to the convergence reward of vanilla MADDPG with 1/4 realistic time, and its convergence beats the original model by a significant margin. Our ablation studies show that experience augmentation is a crucial ingredient which accelerates the training process and boosts the convergence.

We introduce a random forest approach to enable spreads' prediction in the primary catastrophe bond market. We investigate whether all information provided to investors in the offering circular prior to a new issuance is equally important in predicting its spread. The whole population of non-life catastrophe bonds issued from December 2009 to May 2018 is used. The random forest shows an impressive predictive power on unseen primary catastrophe bond data explaining 93% of the total variability. For comparison, linear regression, our benchmark model, has inferior predictive performance explaining only 47% of the total variability. All details provided in the offering circular are predictive of spread but in a varying degree. The stability of the results is studied. The usage of random forest can speed up investment decisions in the catastrophe bond industry.