Most reinforcement learning algorithms take advantage of an experience replay buffer to repeatedly train on samples the agent has observed in the past. Not all samples carry the same amount of significance and simply assigning equal importance to each of the samples is a naive strategy. In this paper, we propose a method to prioritize samples based on how much we can learn from a sample. We define the learn-ability of a sample as the steady decrease of the training loss associated with this sample over time. We develop an algorithm to prioritize samples with high learn-ability, while assigning lower priority to those that are hard-to-learn, typically caused by noise or stochasticity. We empirically show that across multiple domains our method is more robust than random sampling and also better than just prioritizing with respect to the training loss, i.e. the temporal difference loss, which is used in prioritized experience replay. The code to reproduce our experiments can be found here.

Mobile health aims to enhance health outcomes by delivering interventions to individuals as they go about their daily life. The involvement of care partners and social support networks often proves crucial in helping individuals managing burdensome medical conditions. This presents opportunities in mobile health to design interventions that target the dyadic relationship -- the relationship between a target person and their care partner -- with the aim of enhancing social support. In this paper, we develop dyadic RL, an online reinforcement learning algorithm designed to personalize intervention delivery based on contextual factors and past responses of a target person and their care partner. Here, multiple sets of interventions impact the dyad across multiple time intervals. The developed dyadic RL is Bayesian and hierarchical. We formally introduce the problem setup, develop dyadic RL and establish a regret bound. We demonstrate dyadic RL's empirical performance through simulation studies on both toy scenarios and on a realistic test bed constructed from data collected in a mobile health study.

We revisit the fundamental question of simple-versus-simple hypothesis testing with an eye towards computational complexity, as the statistically optimal likelihood ratio test is often computationally intractable in high-dimensional settings. In the classical spiked Wigner model (with a general i.i.d. spike prior) we show that an existing test based on linear spectral statistics achieves the best possible tradeoff curve between type I and type II error rates among all computationally efficient tests, even though there are exponential-time tests that do better. This result is conditional on an appropriate complexity-theoretic conjecture, namely a natural strengthening of the well-established low-degree conjecture. Our result shows that the spectrum is a sufficient statistic for computationally bounded tests (but not for all tests). To our knowledge, our approach gives the first tool for reasoning about the precise asymptotic testing error achievable with efficient computation. The main ingredients required for our hardness result are a sharp bound on the norm of the low-degree likelihood ratio along with (counterintuitively) a positive result on achievability of testing. This strategy appears to be new even in the setting of unbounded computation, in which case it gives an alternate way to analyze the fundamental statistical limits of testing.

This book aims to provide an introduction to the topic of deep learning algorithms. We review essential components of deep learning algorithms in full mathematical detail including different artificial neural network (ANN) architectures (such as fully-connected feedforward ANNs, convolutional ANNs, recurrent ANNs, residual ANNs, and ANNs with batch normalization) and different optimization algorithms (such as the basic stochastic gradient descent (SGD) method, accelerated methods, and adaptive methods). We also cover several theoretical aspects of deep learning algorithms such as approximation capacities of ANNs (including a calculus for ANNs), optimization theory (including Kurdyka-{\L}ojasiewicz inequalities), and generalization errors. In the last part of the book some deep learning approximation methods for PDEs are reviewed including physics-informed neural networks (PINNs) and deep Galerkin methods. We hope that this book will be useful for students and scientists who do not yet have any background in deep learning at all and would like to gain a solid foundation as well as for practitioners who would like to obtain a firmer mathematical understanding of the objects and methods considered in deep learning.

Model pruning is a popular approach to enable the deployment of large deep learning models on edge devices with restricted computational or storage capacities. Although sparse models achieve performance comparable to that of their dense counterparts at the level of the entire dataset, they exhibit high accuracy drops for some data sub-groups. Existing methods to mitigate this disparate impact induced by pruning (i) rely on surrogate metrics that address the problem indirectly and have limited interpretability; or (ii) scale poorly with the number of protected sub-groups in terms of computational cost. We propose a constrained optimization approach that directly addresses the disparate impact of pruning: our formulation bounds the accuracy change between the dense and sparse models, for each subgroup. This choice of constraints provides an interpretable success criterion to determine if a pruned model achieves acceptable disparity levels. Experimental results demonstrate that our technique scales reliably to problems involving large models and hundreds of protected sub-groups. Current deep learning practice displays a trend towards larger architectures (Bommasani et al., 2021), as exemplified by popular models such as GPT-4 (OpenAI, 2023), Llama 2 (Touvron et al., 2023) and DALL-E 2 (Ramesh et al., 2022). Model compression techniques such as pruning (Gale et al., 2019), knowledge distillation (Hinton et al., 2015), or quantization (Gholami et al., 2021) are crucial towards enabling the deployment of large models across a wide range of platforms, including resource-constrained edge devices like smartphones. Despite achieving comparable performance at an aggregate level over the entire dataset, pruned models often exhibit significant accuracy reduction for some data sub-groups (Hooker et al., 2019; 2020; Paganini, 2020). In particular, under-represented groups can suffer high performance degradation while the overall performance remains unaffected, thus exacerbating systemic biases in machine learning models. Tran et al. (2022) refer to this phenomenon as the disparate impact of pruning. Existing mitigation methods face challenges in terms of interpretability and scalability to a large number of sub-groups. Tran et al. (2022) introduce constraints aiming to equalize the loss of the sparse model across sub-groups. However, their approach does not account for the unequal grouplevel performance of the dense model. Moreover, while the loss can be a useful surrogate for training, this method addresses the disparate impact issue indirectly as it focuses on controlling the loss, rather than group-level changes in accuracy. Alternatively, Lin et al. (2022) compute per-group importance scores for every model parameter to determine the weights to be pruned. This approach becomes prohibitively expensive when the model or the number of sub-groups is large.

Passenger clustering based on trajectory records is essential for transportation operators. However, existing methods cannot easily cluster the passengers due to the hierarchical structure of the passenger trip information, including multiple trips within each passenger and multi-dimensional information about each trip. Furthermore, existing approaches rely on an accurate specification of the clustering number to start. Finally, existing methods do not consider spatial semantic graphs such as geographical proximity and functional similarity between the locations. In this paper, we propose a novel tensor Dirichlet Process Multinomial Mixture model with graphs, which can preserve the hierarchical structure of the multi-dimensional trip information and cluster them in a unified one-step manner with the ability to determine the number of clusters automatically. The spatial graphs are utilized in community detection to link the semantic neighbors. We further propose a tensor version of Collapsed Gibbs Sampling method with a minimum cluster size requirement. A case study based on Hong Kong metro passenger data is conducted to demonstrate the automatic process of cluster amount evolution and better cluster quality measured by within-cluster compactness and cross-cluster separateness. The code is available at https://github.com/bonaldli/TensorDPMM-G.

Quantum Recurrent Neural Networks (QRNNs) are robust candidates to model and predict future values in multivariate time series. However, the effective implementation of some QRNN models is limited by the need of mid-circuit measurements. Those increase the requirements for quantum hardware, which in the current NISQ era does not allow reliable computations. Emulation arises as the main near-term alternative to explore the potential of QRNNs, but existing quantum emulators are not dedicated to circuits with multiple intermediate measurements. In this context, we design a specific emulation method that relies on density matrix formalism. The mathematical development is explicitly provided as a compact formulation by using tensor notation. It allows us to show how the present and past information from a time series is transmitted through the circuit, and how to reduce the computational cost in every time step of the emulated network. In addition, we derive the analytical gradient and the Hessian of the network outputs with respect to its trainable parameters, with an eye on gradient-based training and noisy outputs that would appear when using real quantum processors. We finally test the presented methods using a novel hardware-efficient ansatz and three diverse datasets that include univariate and multivariate time series. Our results show how QRNNs can make accurate predictions of future values by capturing non-trivial patterns of input series with different complexities.

The recent explosion of performance of large language models (LLMs) has changed the field of Natural Language Processing (NLP) more abruptly and seismically than any other shift in the field's 80-year history. This has resulted in concerns that the field will become homogenized and resource-intensive. The new status quo has put many academic researchers, especially PhD students, at a disadvantage. This paper aims to define a new NLP playground by proposing 20+ PhD-dissertation-worthy research directions, covering theoretical analysis, new and challenging problems, learning paradigms, and interdisciplinary applications.

Transformer-based models, specifically BERT, have propelled research in various NLP tasks. However, these models are limited to a maximum token limit of 512 tokens. Consequently, this makes it non-trivial to apply it in a practical setting with long input. Various complex methods have claimed to overcome this limit, but recent research questions the efficacy of these models across different classification tasks. These complex architectures evaluated on carefully curated long datasets perform at par or worse than simple baselines. In this work, we propose a relatively simple extension to vanilla BERT architecture called ChunkBERT that allows finetuning of any pretrained models to perform inference on arbitrarily long text. The proposed method is based on chunking token representations and CNN layers, making it compatible with any pre-trained BERT. We evaluate chunkBERT exclusively on a benchmark for comparing long-text classification models across a variety of tasks (including binary classification, multi-class classification, and multi-label classification). A BERT model finetuned using the ChunkBERT method performs consistently across long samples in the benchmark while utilizing only a fraction (6.25\%) of the original memory footprint. These findings suggest that efficient finetuning and inference can be achieved through simple modifications to pre-trained BERT models.

Automated parking is a self-driving feature that has been in cars for several years. Parking assistants in currently sold cars fail to park in more complex real-world scenarios and require the driver to move the car to an expected starting position before the assistant is activated. We overcome these limitations by proposing a planning algorithm consisting of two stages: (1) a geometric planner for maneuvering inside the parking slot and (2) a Rapidly-exploring Random Trees (RRT)-based planner that finds a collision-free path from the initial position to the slot entry. Evaluation of computational experiments demonstrates that improvements over commonly used RRT extensions reduce the parking path cost by 21 % and reduce the computation time by 79.5 %. The suitability of the algorithm for real-world parking scenarios was verified in physical experiments with Porsche Cayenne.