Meta-learning enables quick adaptation of machine learning models to new tasks with limited data. While tasks could come from varying distributions in reality, most of the existing meta-learning methods consider both training and testing tasks as from the same uni-component distribution, overlooking two critical needs of a practical solution: (1) the various sources of tasks may compose a multi-component mixture distribution, and (2) novel tasks may come from a distribution that is unseen during meta-training. In this paper, we demonstrate these two challenges can be solved jointly by modeling the density of task instances. We develop a meta-training framework underlain by a novel Hierarchical Gaussian Mixture based Task Generative Model (HTGM). HTGM extends the widely used empirical process of sampling tasks to a theoretical model, which learns task embeddings, fits the mixture distribution of tasks, and enables density-based scoring of novel tasks. The framework is agnostic to the encoder and scales well with large backbone networks. The model parameters are learned end-to-end by maximum likelihood estimation via an Expectation-Maximization (EM) algorithm. Extensive experiments on benchmark datasets indicate the effectiveness of our method for both sample classification and novel task detection.

A common challenge faced in practical supervised learning, such as medical image processing and robotic interactions, is that there are plenty of tasks but each task cannot afford to collect enough labeled examples to be learned in isolation. However, by exploiting the similarities across those tasks, one can hope to overcome such data scarcity. Under a canonical scenario where each task is drawn from a mixture of $k$ linear regressions, we study a fundamental question: can abundant small-data tasks compensate for the lack of big-data tasks? Existing second moment based approaches of \cite{2020arXiv200208936K} show that such a trade-off is efficiently achievable, with the help of medium-sized tasks with $\Omega(k^{1/2})$ examples each. However, this algorithm is brittle in two important scenarios.

Financial time series forecasting in zero-shot settings is critical for investment decisions, especially during abrupt market regime shifts or in emerging markets with limited historical data. While Model-Agnostic Meta-Learning (MAML) approaches show promise, existing meta-task construction strategies often yield suboptimal performance for highly turbulent financial series. To address this, we propose a novel task-construction method that leverages learned embeddings for both meta task and also downstream predictions, enabling effective zero-shot meta-learning. Specifically, we use Gaussian Mixture Models (GMMs) to softly cluster embeddings, constructing two complementary meta-task types: intra-cluster tasks and inter-cluster tasks. By assigning embeddings to multiple latent regimes probabilistically, GMMs enable richer, more diverse meta-learning. This dual approach ensures the model can quickly adapt to local patterns while simultaneously capturing invariant cross-series features. Furthermore, we enhance inter-cluster generalization through hard task mining, which identifies robust patterns across divergent market regimes. Our method was validated using real-world financial data from high-volatility periods and multiple international markets (including emerging markets). The results demonstrate significant out-performance over existing approaches and stronger generalization in zero-shot scenarios.

More specifically, suppose we deal with n linear regression data sets after which we are challenged with a final learning task of linear regression, but the parameters of these "tasks" are not completely unrelated. In particular, suppose there is a prior distribution (with at most k possible outcomes) from which parameters of linear regression (i.e., the linear function and noise's variance) are sampled. The general idea here is that by learning from "different" (yet related) tasks the learner aims to do better on the final task, and the paper's focus is on a theoretically natural setting.

The reviewers uniformly felt that this is an interesting paper and a good contribution to the community.

Meta-learning enables quick adaptation of machine learning models to new tasks with limited data. While tasks could come from varying distributions in reality, most of the existing meta-learning methods consider both training and testing tasks as from the same uni-component distribution, overlooking two critical needs of a practical solution: (1) the various sources of tasks may compose a multi-component mixture distribution, and (2) novel tasks may come from a distribution that is unseen during meta-training. In this paper, we demonstrate these two challenges can be solved jointly by modeling the density of task instances. We develop a meta-training framework underlain by a novel Hierarchical Gaussian Mixture based Task Generative Model (HTGM). HTGM extends the widely used empirical process of sampling tasks to a theoretical model, which learns task embeddings, fits the mixture distribution of tasks, and enables density-based scoring of novel tasks.

A common challenge faced in practical supervised learning, such as medical image processing and robotic interactions, is that there are plenty of tasks but each task cannot afford to collect enough labeled examples to be learned in isolation. However, by exploiting the similarities across those tasks, one can hope to overcome such data scarcity. Under a canonical scenario where each task is drawn from a mixture of k linear regressions, we study a fundamental question: can abundant small-data tasks compensate for the lack of big-data tasks? Existing second moment based approaches of \cite{2020arXiv200208936K} show that such a trade-off is efficiently achievable, with the help of medium-sized tasks with \Omega(k {1/2}) examples each. However, this algorithm is brittle in two important scenarios.

Trajectory planners of autonomous vehicles usually rely on physical models to predict the vehicle behavior. However, despite their suitability, physical models have some shortcomings. On the one hand, simple models suffer from larger model errors and more restrictive assumptions. On the other hand, complex models are computationally more demanding and depend on environmental and operational parameters. In each case, the drawbacks can be associated to a certain degree to the physical modeling of the yaw rate dynamics. Therefore, this paper investigates the yaw rate prediction based on conditional neural processes (CNP), a data-driven meta-learning approach, to simultaneously achieve low errors, adequate complexity and robustness to varying parameters. Thus, physical models can be enhanced in a targeted manner to provide accurate and computationally efficient predictions to enable safe planning in autonomous vehicles. High fidelity simulations for a variety of driving scenarios and different types of cars show that CNP makes it possible to employ and transfer knowledge about the yaw rate based on current driving dynamics in a human-like manner, yielding robustness against changing environmental and operational conditions.