The paper presents a new efficient and robust method for rare event probability estimation for computational models of an engineering product or a process returning categorical information only, for example, either success or failure. For such models, most of the methods designed for the estimation of failure probability, which use the numerical value of the outcome to compute gradients or to estimate the proximity to the failure surface, cannot be applied. Even if the performance function provides more than just binary output, the state of the system may be a non-smooth or even a discontinuous function defined in the domain of continuous input variables. In these cases, the classical gradient-based methods usually fail. We propose a simple yet efficient algorithm, which performs a sequential adaptive selection of points from the input domain of random variables to extend and refine a simple distance-based surrogate model. Two different tasks can be accomplished at any stage of sequential sampling: (i) estimation of the failure probability, and (ii) selection of the best possible candidate for the subsequent model evaluation if further improvement is necessary. The proposed criterion for selecting the next point for model evaluation maximizes the expected probability classified by using the candidate. Therefore, the perfect balance between global exploration and local exploitation is maintained automatically. The method can estimate the probabilities of multiple failure types. Moreover, when the numerical value of model evaluation can be used to build a smooth surrogate, the algorithm can accommodate this information to increase the accuracy of the estimated probabilities. Lastly, we define a new simple yet general geometrical measure of the global sensitivity of the rare-event probability to individual variables, which is obtained as a by-product of the proposed algorithm.

Smart eHealth applications deliver personalized and preventive digital healthcare services to clients through remote sensing, continuous monitoring, and data analytics. Smart eHealth applications sense input data from multiple modalities, transmit the data to edge and/or cloud nodes, and process the data with compute intensive machine learning (ML) algorithms. Run-time variations with continuous stream of noisy input data, unreliable network connection, computational requirements of ML algorithms, and choice of compute placement among sensor-edge-cloud layers affect the efficiency of ML-driven eHealth applications. In this chapter, we present edge-centric techniques for optimized compute placement, exploration of accuracy-performance trade-offs, and cross-layered sense-compute co-optimization for ML-driven eHealth applications. We demonstrate the practical use cases of smart eHealth applications in everyday settings, through a sensor-edge-cloud framework for an objective pain assessment case study.

Estimating forest AGB at large scales and fine spatial resolutions has become increasingly important for greenhouse gas accounting, monitoring, and verification efforts to mitigate climate change. Airborne LiDAR is highly valuable for modeling attributes of forest structure including AGB, yet most LiDAR collections take place at local or regional scales covering irregular, non-contiguous footprints, resulting in a patchwork of different landscape segments at various points in time. Here, as part of a statewide forest carbon assessment for New York State (USA), we addressed common obstacles in leveraging a LiDAR patchwork for AGB mapping at landscape scales, including selection of training data, the investigation of regional or coverage specific patterns in prediction error, and map agreement with field inventory across multiple scales. Three machine learning algorithms and an ensemble model were trained with FIA field measurements, airborne LiDAR, and topographic, climatic and cadastral geodata. Using a strict set of plot selection criteria, 801 FIA plots were selected with co-located point clouds drawn from a patchwork of 17 leaf-off LiDAR coverages (2014-2019). Our ensemble model was used to produce 30 m AGB prediction surfaces within a predictor-defined area of applicability (98% of LiDAR coverage), and the resulting AGB maps were compared with FIA plot-level and areal estimates at multiple scales of aggregation. Our model was overall accurate (% RMSE 22-45%; MAE 11.6-29.4 Mg ha$^{-1}$; ME 2.4-6.3 Mg ha$^{-1}$), explained 73-80% of field-observed variation, and yielded estimates that were consistent with FIA's design-based estimates (89% of estimates within FIA's 95% CI). We share practical solutions to challenges faced in using spatiotemporal patchworks of LiDAR to meet growing needs for AGB mapping in support of applications in forest carbon accounting and ecosystem.

We investigate nonlinear prediction in an online setting and introduce a hybrid model that effectively mitigates, via an end-to-end architecture, the need for hand-designed features and manual model selection issues of conventional nonlinear prediction/regression methods. In particular, we use recursive structures to extract features from sequential signals, while preserving the state information, i.e., the history, and boosted decision trees to produce the final output. The connection is in an end-to-end fashion and we jointly optimize the whole architecture using stochastic gradient descent, for which we also provide the backward pass update equations. In particular, we employ a recurrent neural network (LSTM) for adaptive feature extraction from sequential data and a gradient boosting machinery (soft GBDT) for effective supervised regression. Our framework is generic so that one can use other deep learning architectures for feature extraction (such as RNNs and GRUs) and machine learning algorithms for decision making as long as they are differentiable. We demonstrate the learning behavior of our algorithm on synthetic data and the significant performance improvements over the conventional methods over various real life datasets. Furthermore, we openly share the source code of the proposed method to facilitate further research.

This work establishes low test error of gradient flow (GF) and stochastic gradient descent (SGD) on two-layer ReLU networks with standard initialization, in three regimes where key sets of weights rotate little (either naturally due to GF and SGD, or due to an artificial constraint), and making use of margins as the core analytic technique. The first regime is near initialization, specifically until the weights have moved by $\mathcal{O}(\sqrt m)$, where $m$ denotes the network width, which is in sharp contrast to the $\mathcal{O}(1)$ weight motion allowed by the Neural Tangent Kernel (NTK); here it is shown that GF and SGD only need a network width and number of samples inversely proportional to the NTK margin, and moreover that GF attains at least the NTK margin itself, which suffices to establish escape from bad KKT points of the margin objective, whereas prior work could only establish nondecreasing but arbitrarily small margins. The second regime is the Neural Collapse (NC) setting, where data lies in extremely-well-separated groups, and the sample complexity scales with the number of groups; here the contribution over prior work is an analysis of the entire GF trajectory from initialization. Lastly, if the inner layer weights are constrained to change in norm only and can not rotate, then GF with large widths achieves globally maximal margins, and its sample complexity scales with their inverse; this is in contrast to prior work, which required infinite width and a tricky dual convergence assumption. As purely technical contributions, this work develops a variety of potential functions and other tools which will hopefully aid future work.

Density estimation is a fundamental task in statistics and machine learning applications. Kernel density estimation is a powerful tool for non-parametric density estimation in low dimensions; however, its performance is poor in higher dimensions. Moreover, its prediction complexity scale linearly with more training data points. This paper presents a method for neural density estimation that can be seen as a type of kernel density estimation, but without the high prediction computational complexity. The method is based on density matrices, a formalism used in quantum mechanics, and adaptive Fourier features. The method can be trained without optimization, but it could be also integrated with deep learning architectures and trained using gradient descent. Thus, it could be seen as a form of neural density estimation method. The method was evaluated in different synthetic and real datasets, and its performance compared against state-of-the-art neural density estimation methods, obtaining competitive results.

We consider the setting where a master wants to run a distributed stochastic gradient descent (SGD) algorithm on $n$ workers, each having a subset of the data. Distributed SGD may suffer from the effect of stragglers, i.e., slow or unresponsive workers who cause delays. One solution studied in the literature is to wait at each iteration for the responses of the fastest $k

Meta-learning from learning curves is an important yet often neglected research area in the Machine Learning community. We introduce a series of Reinforcement Learning-based meta-learning challenges, in which an agent searches for the best suited algorithm for a given dataset, based on feedback of learning curves from the environment. The first round attracted participants both from academia and industry. This paper analyzes the results of the first round (accepted to the competition program of WCCI 2022), to draw insights into what makes a meta-learner successful at learning from learning curves. With the lessons learned from the first round and the feedback from the participants, we have designed the second round of our challenge with a new protocol and a new meta-dataset. The second round of our challenge is accepted at the AutoML-Conf 2022 and currently ongoing .

Motivated by practical needs of experimentation and policy learning in online platforms, we study the problem of safe data collection. Specifically, our goal is to develop a logging policy that efficiently explores different actions to elicit information while achieving competitive reward with a baseline production policy. We first show that a common practice of mixing the production policy with randomized exploration, despite being safe, is sub-optimal in maximizing information gain. Then, we propose a safe optimal logging policy via a novel water-filling technique for the case when no side information about the actions' expected reward is available. We improve upon this design by considering side information and also extend our approaches to the linear contextual model to account for a large number of actions. Along the way, we analyze how our data logging policies impact errors in off(line)-policy learning and empirically validate the benefit of our design by conducting extensive numerical experiments with synthetic and MNIST datasets. To further demonstrate the generality of our approach, we also consider the safe online learning setting. By adaptively applying our techniques, we develop the Safe Phased-Elimination (SafePE) algorithm that can achieve optimal regret bound with only logarithmic number of policy updates.

Federated learning (FL) has been recognized as one of the most promising solutions for distributed machine learning (ML). In most of the current literature, FL has been studied for supervised ML tasks, in which edge devices collect labeled data. Nevertheless, in many applications, it is impractical to assume existence of labeled data across devices. To this end, we develop a novel methodology, Cooperative Federated unsupervised Contrastive Learning (CF-CL), for FL across edge devices with unlabeled datasets. CF-CL employs local device cooperation where data are exchanged among devices through device-to-device (D2D) communications to avoid local model bias resulting from non-independent and identically distributed (non-i.i.d.) local datasets. CF-CL introduces a push-pull smart data sharing mechanism tailored to unsupervised FL settings, in which, each device pushes a subset of its local datapoints to its neighbors as reserved data points, and pulls a set of datapoints from its neighbors, sampled through a probabilistic importance sampling technique. We demonstrate that CF-CL leads to (i) alignment of unsupervised learned latent spaces across devices, (ii) faster global convergence, allowing for less frequent global model aggregations; and (iii) is effective in extreme non-i.i.d. data settings across the devices.