We address the challenge of constructing valid confidence intervals and sets in problems of prediction across multiple environments. We investigate two types of coverage suitable for these problems, extending the jackknife and split-conformal methods to show how to obtain distribution-free coverage in such non-traditional, hierarchical data-generating scenarios. Our contributions also include extensions for settings with non-real-valued responses and a theory of consistency for predictive inference in these general problems. We demonstrate a novel resizing method to adapt to problem difficulty, which applies both to existing approaches for predictive inference with hierarchical data and the methods we develop; this reduces prediction set sizes using limited information from the test environment, a key to the methods' practical performance, which we evaluate through neurochemical sensing and species classification datasets.

Recent research underscores the pivotal role of the Out-of-Distribution (OOD) feature representation field scale in determining the efficacy of models in OOD detection. Consequently, the adoption of model ensembles has emerged as a prominent strategy to augment this feature representation field, capitalizing on anticipated model diversity. However, our introduction of novel qualitative and quantitative model ensemble evaluation methods, specifically Loss Basin/Barrier Visualization and the Self-Coupling Index, reveals a critical drawback in existing ensemble methods. We find that these methods incorporate weights that are affine-transformable, exhibiting limited variability and thus failing to achieve the desired diversity in feature representation. To address this limitation, we elevate the dimensions of traditional model ensembles, incorporating various factors such as different weight initializations, data holdout, etc., into distinct supervision tasks. This innovative approach, termed Multi-Comprehension (MC) Ensemble, leverages diverse training tasks to generate distinct comprehensions of the data and labels, thereby extending the feature representation field. Our experimental results demonstrate the superior performance of the MC Ensemble strategy in OOD detection compared to both the naive Deep Ensemble method and a standalone model of comparable size. This underscores the effectiveness of our proposed approach in enhancing the model's capability to detect instances outside its training distribution.

Compared to supervised learning algorithms that only use labeled data, semi-supervised learning algorithms can fully utilize the information from unlabeled data, thereby improving classification performance. Classic semi-supervised learning classification algorithms include Semi-Supervised Support Vector Machines (S3VM), Self-Training algorithms, Generative Classification Models, and Label Propagation Algorithms. Below, we provide an overview of these algorithms. Semi-Supervised Support Vector Machines(S3VM) is based on the principles of traditional Support Vector Machines (SVM), aiming to find a hyperplane that separates data from different classes while maintaining the maximum margin possible. Unlike traditional SVM, S3VM incorporates unlabeled data to fully utilize this additional information(See [1]). In the optimization objective function, S3VM minimizes misclassification of labeled data and boundary violations of unlabeled data. The goal is to maintain the accuracy of labeled data classification while leveraging the information from unlabeled data to improve classification performance. However, S3VM still suffers from assumptions about unlabeled data and potential issues such as local optima.

Directed acyclic graphs (DAGs) are widely used to capture causal relationships among components of complex systems (Spirtes et al., 2001; Pearl, 2009; Maathuis et al., 2018). They also form a foundation for causal discovery and inference (Pearl, 2009). Probabilistic graphical models defined on DAGs, known as Bayesian networks (Pearl, 2009), have thus found broad applications in various scientific disciplines, from biology (Markowetz and Spang, 2007; Zhang et al., 2013) and social sciences (Gupta and Kim, 2008), to knowledge representation and machine learning (Heckerman, 1997). However, learning the structure of DAGs from observational data is very challenging due to at least two major factors: First, it may not be possible to infer the direction of edges from observational data alone. In fact, unless the model is identifiable (see, e.g., Peters et al., 2014a), observational data only reveal the structure of the Markov equivalent class of DAGs (Maathuis et al., 2018), captured by a complete partially directed acyclic graph (CPDAG) (Andersson et al., 1997). The second reason is computational--learning DAGs from observational data is an NPcomplete problem (Chickering, 1996). In fact, while a few polynomial time algorithms have been proposed for special cases, including sparse graphs (Kalisch and Bühlmann, 2007) or identifiable models (Chen et al., 2019; Ghoshal and Honorio, 2018; Peters et al., 2014b; Wang and Drton, 2020; Shimizu et al., 2006; Yu et al., 2023), existing general-purpose algorithms are not scalable to problems involving many variables. In spite of the many challenges of learning DAGs in general settings, the problem becomes very manageable if a valid causal ordering among variables is known (Shojaie and Michailidis, 2010). In a valid causal ordering for a DAG G with node set V, any node j can appear before another node k (denoted j k) only if there is no directed path from k to j.

Recent work shows that path gradient estimators for normalizing flows have lower variance compared to standard estimators for variational inference, resulting in improved training. However, they are often prohibitively more expensive from a computational point of view and cannot be applied to maximum likelihood training in a scalable manner, which severely hinders their widespread adoption. In this work, we overcome these crucial limitations. Specifically, we propose a fast path gradient estimator which improves computational efficiency significantly and works for all normalizing flow architectures of practical relevance. We then show that this estimator can also be applied to maximum likelihood training for which it has a regularizing effect as it can take the form of a given target energy function into account. We empirically establish its superior performance and reduced variance for several natural sciences applications.

Domain generalization aims at learning a universal model that performs well on unseen target domains, incorporating knowledge from multiple source domains. In this research, we consider the scenario where different domain shifts occur among conditional distributions of different classes across domains. When labeled samples in the source domains are limited, existing approaches are not sufficiently robust. To address this problem, we propose a novel domain generalization framework called {Wasserstein Distributionally Robust Domain Generalization} (WDRDG), inspired by the concept of distributionally robust optimization. We encourage robustness over conditional distributions within class-specific Wasserstein uncertainty sets and optimize the worst-case performance of a classifier over these uncertainty sets. We further develop a test-time adaptation module leveraging optimal transport to quantify the relationship between the unseen target domain and source domains to make adaptive inference for target data. Experiments on the Rotated MNIST, PACS and the VLCS datasets demonstrate that our method could effectively balance the robustness and discriminability in challenging generalization scenarios.

This paper introduces a model-based approach for training feedback controllers for an autonomous agent operating in a highly nonlinear environment. We desire the trained policy to ensure that the agent satisfies specific task objectives, expressed in discrete-time Signal Temporal Logic (DT-STL). One advantage for reformulation of a task via formal frameworks, like DT-STL, is that it permits quantitative satisfaction semantics. In other words, given a trajectory and a DT-STL formula, we can compute the robustness, which can be interpreted as an approximate signed distance between the trajectory and the set of trajectories satisfying the formula. We utilize feedback controllers, and we assume a feed forward neural network for learning these feedback controllers. We show how this learning problem is similar to training recurrent neural networks (RNNs), where the number of recurrent units is proportional to the temporal horizon of the agent's task objectives. This poses a challenge: RNNs are susceptible to vanishing and exploding gradients, and na\"{i}ve gradient descent-based strategies to solve long-horizon task objectives thus suffer from the same problems. To tackle this challenge, we introduce a novel gradient approximation algorithm based on the idea of dropout or gradient sampling. We show that, the existing smooth semantics for robustness are inefficient regarding gradient computation when the specification becomes complex. To address this challenge, we propose a new smooth semantics for DT-STL that under-approximates the robustness value and scales well for backpropagation over a complex specification. We show that our control synthesis methodology, can be quite helpful for stochastic gradient descent to converge with less numerical issues, enabling scalable backpropagation over long time horizons and trajectories over high dimensional state spaces.

The focus of recent research has shifted from merely improving the metrics based performance of Deep Neural Networks (DNNs) to DNNs which are more interpretable to humans. The field of eXplainable Artificial Intelligence (XAI) has observed various techniques, including saliency-based and concept-based approaches. These approaches explain the model's decisions in simple human understandable terms called Concepts. Concepts are known to be the thinking ground of humans}. Explanations in terms of concepts enable detecting spurious correlations, inherent biases, or clever-hans. With the advent of concept-based explanations, a range of concept representation methods and automatic concept discovery algorithms have been introduced. Some recent works also use concepts for model improvement in terms of interpretability and generalization. We provide a systematic review and taxonomy of various concept representations and their discovery algorithms in DNNs, specifically in vision. We also provide details on concept-based model improvement literature marking the first comprehensive survey of these methods.

Analytic features in gambling study are performed based on the amount of data monitoring on user daily actions. While performing the detection of problem gambling, existing datasets provide relatively rich analytic features for building machine learning based model. However, considering the complexity and cost of collecting the analytic features in real applications, conducting precise detection with less features will tremendously reduce the cost of data collection. In this study, we propose a deep neural networks PGN4 that performs well when using limited analytic features. Through the experiment on two datasets, we discover that PGN4 only experiences a mere performance drop when cutting 102 features to 5 features. Besides, we find the commonality within the top 5 features from two datasets.

Current federated learning (FL) approaches view decentralized training data as a single table, divided among participants either horizontally (by rows) or vertically (by columns). However, these approaches are inadequate for handling distributed relational tables across databases. This scenario requires intricate SQL operations like joins and unions to obtain the training data, which is either costly or restricted by privacy concerns. This raises the question: can we directly run FL on distributed relational tables? In this paper, we formalize this problem as relational federated learning (RFL). We propose TablePuppet, a generic framework for RFL that decomposes the learning process into two steps: (1) learning over join (LoJ) followed by (2) learning over union (LoU). In a nutshell, LoJ pushes learning down onto the vertical tables being joined, and LoU further pushes learning down onto the horizontal partitions of each vertical table. TablePuppet incorporates computation/communication optimizations to deal with the duplicate tuples introduced by joins, as well as differential privacy (DP) to protect against both feature and label leakages. We demonstrate the efficiency of TablePuppet in combination with two widely-used ML training algorithms, stochastic gradient descent (SGD) and alternating direction method of multipliers (ADMM), and compare their computation/communication complexity. We evaluate the SGD/ADMM algorithms developed atop TablePuppet by training diverse ML models. Our experimental results show that TablePuppet achieves model accuracy comparable to the centralized baselines running directly atop the SQL results. Moreover, ADMM takes less communication time than SGD to converge to similar model accuracy.