Thanks to their easy implementation via Radial Basis Functions (RBFs), meshfree kernel methods have been proved to be an effective tool for e.g. scattered data interpolation, PDE collocation, classification and regression tasks. Their accuracy might depend on a length scale hyperparameter, which is often tuned via cross validation schemes. Here we leverage approaches and tools from the machine learning community to introduce two-layered kernel machines, which generalize the classical RBF approaches that rely on a single hyperparameter. Indeed, the proposed learning strategy returns a kernel that is optimized not only in the Euclidean directions, but that further incorporates kernel rotations. The kernel optimization is shown to be robust by using recently improved calculations of cross validation scores. Finally, the use of greedy approaches, and specifically of the Vectorial Kernel Orthogonal Greedy Algorithm (VKOGA), allows us to construct an optimized basis that adapts to the data. Beyond a rigorous analysis on the convergence of the so-constructed two-Layered (2L)-VKOGA, its benefits are highlighted on both synthesized and real benchmark data sets.
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There are multiple cluster randomised trial designs that vary in when the clusters cross between control and intervention states, when observations are made within clusters, and how many observations are made at that time point. Identifying the most efficient study design is complex though, owing to the correlation between observations within clusters and over time. In this article, we present a review of statistical and computational methods for identifying optimal cluster randomised trial designs. We also adapt methods from the experimental design literature for experimental designs with correlated observations to the cluster trial context. We identify three broad classes of methods: using exact formulae for the treatment effect estimator variance for specific models to derive algorithms or weights for cluster sequences; generalised methods for estimating weights for experimental units; and, combinatorial optimisation algorithms to select an optimal subset of experimental units. We also discuss methods for rounding weights to whole numbers of clusters and extensions to non-Gaussian models. We present results from multiple cluster trial examples that compare the different methods, including problems involving determining optimal allocation of clusters across a set of cluster sequences, and selecting the optimal number of single observations to make in each cluster-period for both Gaussian and non-Gaussian models, and including exchangeable and exponential decay covariance structures.
Distributed Stein Variational Gradient Descent (DSVGD) is a non-parametric distributed learning framework for federated Bayesian learning, where multiple clients jointly train a machine learning model by communicating a number of non-random and interacting particles with the server. Since communication resources are limited, selecting the clients with most informative local learning updates can improve the model convergence and communication efficiency. In this paper, we propose two selection schemes for DSVGD based on Kernelized Stein Discrepancy (KSD) and Hilbert Inner Product (HIP). We derive the upper bound on the decrease of the global free energy per iteration for both schemes, which is then minimized to speed up the model convergence. We evaluate and compare our schemes with conventional schemes in terms of model accuracy, convergence speed, and stability using various learning tasks and datasets.
Inverse reinforcement learning~(IRL) is a powerful framework to infer an agent's reward function by observing its behavior, but IRL algorithms that learn point estimates of the reward function can be misleading because there may be several functions that describe an agent's behavior equally well. A Bayesian approach to IRL models a distribution over candidate reward functions, alleviating the shortcomings of learning a point estimate. However, several Bayesian IRL algorithms use a $Q$-value function in place of the likelihood function. The resulting posterior is computationally intensive to calculate, has few theoretical guarantees, and the $Q$-value function is often a poor approximation for the likelihood. We introduce kernel density Bayesian IRL (KD-BIRL), which uses conditional kernel density estimation to directly approximate the likelihood, providing an efficient framework that, with a modified reward function parameterization, is applicable to environments with complex and infinite state spaces. We demonstrate KD-BIRL's benefits through a series of experiments in Gridworld environments and a simulated sepsis treatment task.
Combining machine learning and constrained optimization, Predict+Optimize tackles optimization problems containing parameters that are unknown at the time of solving. Prior works focus on cases with unknowns only in the objectives. A new framework was recently proposed to cater for unknowns also in constraints by introducing a loss function, called Post-hoc Regret, that takes into account the cost of correcting an unsatisfiable prediction. Since Post-hoc Regret is non-differentiable, the previous work computes only its approximation. While the notion of Post-hoc Regret is general, its specific implementation is applicable to only packing and covering linear programming problems. In this paper, we first show how to compute Post-hoc Regret exactly for any optimization problem solvable by a recursive algorithm satisfying simple conditions. Experimentation demonstrates substantial improvement in the quality of solutions as compared to the earlier approximation approach. Furthermore, we show experimentally the empirical behavior of different combinations of correction and penalty functions used in the Post-hoc Regret of the same benchmarks. Results provide insights for defining the appropriate Post-hoc Regret in different application scenarios.
While current deep learning (DL)-based beamforming techniques have been proved effective in speech separation, they are often designed to process narrow-band (NB) frequencies independently which results in higher computational costs and inference times, making them unsuitable for real-world use. In this paper, we propose DL-based mel-subband spatio-temporal beamformer to perform speech separation in a car environment with reduced computation cost and inference time. As opposed to conventional subband (SB) approaches, our framework uses a mel-scale based subband selection strategy which ensures a fine-grained processing for lower frequencies where most speech formant structure is present, and coarse-grained processing for higher frequencies. In a recursive way, robust frame-level beamforming weights are determined for each speaker location/zone in a car from the estimated subband speech and noise covariance matrices. Furthermore, proposed framework also estimates and suppresses any echoes from the loudspeaker(s) by using the echo reference signals. We compare the performance of our proposed framework to several NB, SB, and full-band (FB) processing techniques in terms of speech quality and recognition metrics. Based on experimental evaluations on simulated and real-world recordings, we find that our proposed framework achieves better separation performance over all SB and FB approaches and achieves performance closer to NB processing techniques while requiring lower computing cost.
Cross-device federated learning (FL) has been well-studied from algorithmic, system scalability, and training speed perspectives. Nonetheless, moving from centralized training to cross-device FL for millions or billions of devices presents many risks, including performance loss, developer inertia, poor user experience, and unexpected application failures. In addition, the corresponding infrastructure, development costs, and return on investment are difficult to estimate. In this paper, we present a device-cloud collaborative FL platform that integrates with an existing machine learning platform, providing tools to measure real-world constraints, assess infrastructure capabilities, evaluate model training performance, and estimate system resource requirements to responsibly bring FL into production. We also present a decision workflow that leverages the FL-integrated platform to comprehensively evaluate the trade-offs of cross-device FL and share our empirical evaluations of business-critical machine learning applications that impact hundreds of millions of users.
Rather than refining individual candidate solutions for a general non-convex optimization problem, by analogy to evolution, we consider minimizing the average loss for a parametric distribution over hypotheses. In this setting, we prove that Fisher-Rao natural gradient descent (FR-NGD) optimally approximates the continuous-time replicator equation (an essential model of evolutionary dynamics) by minimizing the mean-squared error for the relative fitness of competing hypotheses. We term this finding "conjugate natural selection" and demonstrate its utility by numerically solving an example non-convex optimization problem over a continuous strategy space. Next, by developing known connections between discrete-time replicator dynamics and Bayes's rule, we show that when absolute fitness corresponds to the negative KL-divergence of a hypothesis's predictions from actual observations, FR-NGD provides the optimal approximation of continuous Bayesian inference. We use this result to demonstrate a novel method for estimating the parameters of stochastic processes.
Long-tailed classification poses a challenge due to its heavy imbalance in class probabilities and tail-sensitivity risks with asymmetric misprediction costs. Recent attempts have used re-balancing loss and ensemble methods, but they are largely heuristic and depend heavily on empirical results, lacking theoretical explanation. Furthermore, existing methods overlook the decision loss, which characterizes different costs associated with tailed classes. This paper presents a general and principled framework from a Bayesian-decision-theory perspective, which unifies existing techniques including re-balancing and ensemble methods, and provides theoretical justifications for their effectiveness. From this perspective, we derive a novel objective based on the integrated risk and a Bayesian deep-ensemble approach to improve the accuracy of all classes, especially the ``tail". Besides, our framework allows for task-adaptive decision loss which provides provably optimal decisions in varying task scenarios, along with the capability to quantify uncertainty. Finally, We conduct comprehensive experiments, including standard classification, tail-sensitive classification with a new False Head Rate metric, calibration, and ablation studies. Our framework significantly improves the current SOTA even on large-scale real-world datasets like ImageNet.
We hypothesize that due to the greedy nature of learning in multi-modal deep neural networks, these models tend to rely on just one modality while under-fitting the other modalities. Such behavior is counter-intuitive and hurts the models' generalization, as we observe empirically. To estimate the model's dependence on each modality, we compute the gain on the accuracy when the model has access to it in addition to another modality. We refer to this gain as the conditional utilization rate. In the experiments, we consistently observe an imbalance in conditional utilization rates between modalities, across multiple tasks and architectures. Since conditional utilization rate cannot be computed efficiently during training, we introduce a proxy for it based on the pace at which the model learns from each modality, which we refer to as the conditional learning speed. We propose an algorithm to balance the conditional learning speeds between modalities during training and demonstrate that it indeed addresses the issue of greedy learning. The proposed algorithm improves the model's generalization on three datasets: Colored MNIST, Princeton ModelNet40, and NVIDIA Dynamic Hand Gesture.
Time Series Classification (TSC) is an important and challenging problem in data mining. With the increase of time series data availability, hundreds of TSC algorithms have been proposed. Among these methods, only a few have considered Deep Neural Networks (DNNs) to perform this task. This is surprising as deep learning has seen very successful applications in the last years. DNNs have indeed revolutionized the field of computer vision especially with the advent of novel deeper architectures such as Residual and Convolutional Neural Networks. Apart from images, sequential data such as text and audio can also be processed with DNNs to reach state-of-the-art performance for document classification and speech recognition. In this article, we study the current state-of-the-art performance of deep learning algorithms for TSC by presenting an empirical study of the most recent DNN architectures for TSC. We give an overview of the most successful deep learning applications in various time series domains under a unified taxonomy of DNNs for TSC. We also provide an open source deep learning framework to the TSC community where we implemented each of the compared approaches and evaluated them on a univariate TSC benchmark (the UCR/UEA archive) and 12 multivariate time series datasets. By training 8,730 deep learning models on 97 time series datasets, we propose the most exhaustive study of DNNs for TSC to date.
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