We systematically describe the problem of simultaneous surrogate modeling of mixed variables (i.e., continuous, integer and categorical variables) in the Bayesian optimization (BO) context. We provide a unified hybrid model using both Monte-Carlo tree search (MCTS) and Gaussian processes (GP) that encompasses and generalizes multiple state-of-the-art mixed BO surrogates. Based on the architecture, we propose applying a new dynamic model selection criterion among novel candidate families of covariance kernels, including non-stationary kernels and associated families. Different benchmark problems are studied and presented to support the superiority of our model, along with results highlighting the effectiveness of our method compared to most state-of-the-art mixed-variable methods in BO.
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Recent years have witnessed significant success in Gradient Boosting Decision Trees (GBDT) for a wide range of machine learning applications. Generally, a consensus about GBDT's training algorithms is gradients and statistics are computed based on high-precision floating points. In this paper, we investigate an essentially important question which has been largely ignored by the previous literature: how many bits are needed for representing gradients in training GBDT? To solve this mystery, we propose to quantize all the high-precision gradients in a very simple yet effective way in the GBDT's training algorithm. Surprisingly, both our theoretical analysis and empirical studies show that the necessary precisions of gradients without hurting any performance can be quite low, e.g., 2 or 3 bits. With low-precision gradients, most arithmetic operations in GBDT training can be replaced by integer operations of 8, 16, or 32 bits. Promisingly, these findings may pave the way for much more efficient training of GBDT from several aspects: (1) speeding up the computation of gradient statistics in histograms; (2) compressing the communication cost of high-precision statistical information during distributed training; (3) the inspiration of utilization and development of hardware architectures which well support low-precision computation for GBDT training. Benchmarked on CPU, GPU, and distributed clusters, we observe up to 2$\times$ speedup of our simple quantization strategy compared with SOTA GBDT systems on extensive datasets, demonstrating the effectiveness and potential of the low-precision training of GBDT. The code will be released to the official repository of LightGBM.
In Federated Learning (FL), a number of clients or devices collaborate to train a model without sharing their data. Models are optimized locally at each client and further communicated to a central hub for aggregation. While FL is an appealing decentralized training paradigm, heterogeneity among data from different clients can cause the local optimization to drift away from the global objective. In order to estimate and therefore remove this drift, variance reduction techniques have been incorporated into FL optimization recently. However, these approaches inaccurately estimate the clients' drift and ultimately fail to remove it properly. In this work, we propose an adaptive algorithm that accurately estimates drift across clients. In comparison to previous works, our approach necessitates less storage and communication bandwidth, as well as lower compute costs. Additionally, our proposed methodology induces stability by constraining the norm of estimates for client drift, making it more practical for large scale FL. Experimental findings demonstrate that the proposed algorithm converges significantly faster and achieves higher accuracy than the baselines across various FL benchmarks.
Representation learning in recent years has been addressed with self-supervised learning methods. The input data is augmented into two distorted views and an encoder learns the representations that are invariant to distortions -- cross-view prediction. Augmentation is one of the key components in cross-view self-supervised learning frameworks to learn visual representations. This paper presents ExAgt, a novel method to include expert knowledge for augmenting traffic scenarios, to improve the learnt representations without any human annotation. The expert-guided augmentations are generated in an automated fashion based on the infrastructure, the interactions between the EGO and the traffic participants and an ideal sensor model. The ExAgt method is applied in two state-of-the-art cross-view prediction methods and the representations learnt are tested in downstream tasks like classification and clustering. Results show that the ExAgt method improves representation learning compared to using only standard augmentations and it provides a better representation space stability. The code is available at \url{//github.com/lab176344/ExAgt}.
The sample efficiency of Bayesian optimization(BO) is often boosted by Gaussian Process(GP) surrogate models. However, on mixed variable spaces, surrogate models other than GPs are prevalent, mainly due to the lack of kernels which can model complex dependencies across different types of variables. In this paper, we propose the frequency modulated (FM) kernel flexibly modeling dependencies among different types of variables, so that BO can enjoy the further improved sample efficiency. The FM kernel uses distances on continuous variables to modulate the graph Fourier spectrum derived from discrete variables. However, the frequency modulation does not always define a kernel with the similarity measure behavior which returns higher values for pairs of more similar points. Therefore, we specify and prove conditions for FM kernels to be positive definite and to exhibit the similarity measure behavior. In experiments, we demonstrate the improved sample efficiency of GP BO using FM kernels (BO-FM).On synthetic problems and hyperparameter optimization problems, BO-FM outperforms competitors consistently. Also, the importance of the frequency modulation principle is empirically demonstrated on the same problems. On joint optimization of neural architectures and SGD hyperparameters, BO-FM outperforms competitors including Regularized evolution(RE) and BOHB. Remarkably, BO-FM performs better even than RE and BOHB using three times as many evaluations.
Finding a globally optimal Bayesian Network using exhaustive search is a problem with super-exponential complexity, which severely restricts the number of variables that it can work for. We implement a dynamic programming based algorithm with built-in dimensionality reduction and parent set identification. This reduces the search space drastically and can be applied to large-dimensional data. We use what we call generational orderings based search for optimal networks, which is a novel way to efficiently search the space of possible networks given the possible parent sets. The algorithm supports both continuous and categorical data, and categorical as well as survival outcomes. We demonstrate the efficacy of our algorithm on both synthetic and real data. In simulations, our algorithm performs better than three state-of-art algorithms that are currently used extensively. We then apply it to an Ovarian Cancer gene expression dataset with 513 genes and a survival outcome. Our algorithm is able to find an optimal network describing the disease pathway consisting of 6 genes leading to the outcome node in a few minutes on a basic computer. Our generational orderings based search for optimal networks, is both efficient and highly scalable approach to finding optimal Bayesian Networks, that can be applied to 1000s of variables. Using specifiable parameters - correlation, FDR cutoffs, and in-degree - one can increase or decrease the number of nodes and density of the networks. Availability of two scoring option-BIC and Bge-and implementation of survival outcomes and mixed data types makes our algorithm very suitable for many types of high dimensional biomedical data to find disease pathways.
Zeroth-order optimization methods are developed to overcome the practical hurdle of having knowledge of explicit derivatives. Instead, these schemes work with merely access to noisy functions evaluations. The predominant approach is to mimic first-order methods by means of some gradient estimator. The theoretical limitations are well-understood, yet, as most of these methods rely on finite-differencing for shrinking differences, numerical cancellation can be catastrophic. The numerical community developed an efficient method to overcome this by passing to the complex domain. This approach has been recently adopted by the optimization community and in this work we analyze the practically relevant setting of dealing with computational noise. To exemplify the possibilities we focus on the strongly-convex optimization setting and provide a variety of non-asymptotic results, corroborated by numerical experiments, and end with local non-convex optimization.
Score-based diffusion models provide a powerful way to model images using the gradient of the data distribution. Leveraging the learned score function as a prior, here we introduce a way to sample data from a conditional distribution given the measurements, such that the model can be readily used for solving inverse problems in imaging, especially for accelerated MRI. In short, we train a continuous time-dependent score function with denoising score matching. Then, at the inference stage, we iterate between numerical SDE solver and data consistency projection step to achieve reconstruction. Our model requires magnitude images only for training, and yet is able to reconstruct complex-valued data, and even extends to parallel imaging. The proposed method is agnostic to sub-sampling patterns, and can be used with any sampling schemes. Also, due to its generative nature, our approach can quantify uncertainty, which is not possible with standard regression settings. On top of all the advantages, our method also has very strong performance, even beating the models trained with full supervision. With extensive experiments, we verify the superiority of our method in terms of quality and practicality.
Behavioral models enable the analysis of the functionality of software product lines (SPL), e.g., model checking and model-based testing. Model learning aims at constructing behavioral models for software systems in some form of a finite state machine. Due to the commonalities among the products of an SPL, it is possible to reuse the previously learned models during the model learning process. In this paper, an adaptive approach (the $\text{PL}^*$ method) for learning the product models of an SPL is presented based on the well-known $L^*$ algorithm. In this method, after model learning of each product, the sequences in the final observation table are stored in a repository which will be used to initialize the observation table of the remaining products to be learned. The proposed algorithm is evaluated on two open-source SPLs and the total learning cost is measured in terms of the number of rounds, the total number of resets and input symbols. The results show that for complex SPLs, the total learning cost for the $\text{PL}^*$ method is significantly lower than that of the non-adaptive learning method in terms of all three metrics. Furthermore, it is observed that the order in which the products are learned affects the efficiency of the $\text{PL}^*$ method. Based on this observation, we introduced a heuristic to determine an ordering which reduces the total cost of adaptive learning in both case studies.
Learning new representations of 3D point clouds is an active research area in 3D vision, as the order-invariant point cloud structure still presents challenges to the design of neural network architectures. Recent works explored learning either global or local features or both for point clouds, however none of the earlier methods focused on capturing contextual shape information by analysing local orientation distribution of points. In this paper, we leverage on point orientation distributions around a point in order to obtain an expressive local neighborhood representation for point clouds. We achieve this by dividing the spherical neighborhood of a given point into predefined cone volumes, and statistics inside each volume are used as point features. In this way, a local patch can be represented by not only the selected point's nearest neighbors, but also considering a point density distribution defined along multiple orientations around the point. We are then able to construct an orientation distribution function (ODF) neural network that involves an ODFBlock which relies on mlp (multi-layer perceptron) layers. The new ODFNet model achieves state-of the-art accuracy for object classification on ModelNet40 and ScanObjectNN datasets, and segmentation on ShapeNet S3DIS datasets.
In this paper, we are interested in linear prediction of a particular kind of stochastic process, namely a marked temporal point process. The observations are event times recorded on the real line, with marks attached to each event. We show that in this case, linear prediction extends straightforwardly from the theory of prediction for stationary stochastic processes. Following classical lines, we derive a Wiener-Hopf-type integral equation to characterise the linear predictor, extending the "model independent origin" of the Hawkes process (Jaisson, 2015) as a corollary. We propose two recursive methods to solve the linear prediction problem and show that these are computationally efficient in known cases. The first solves the Wiener-Hopf equation via a set of differential equations. It is particularly well-adapted to autoregressive processes. In the second method, we develop an innovations algorithm tailored for moving-average processes. A small simulation study on two typical examples shows the application of numerical schemes for estimation of a Hawkes process intensity.
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