Bayesian optimization (BO) is a sample-efficient method and has been widely used for optimizing expensive black-box functions. Recently, there has been a considerable interest in BO literature in optimizing functions that are affected by context variable in the environment, which is uncontrollable by decision makers. In this paper, we focus on the optimization of functions' expectations over continuous context variable, subject to an unknown distribution. To address this problem, we propose two algorithms that employ kernel density estimation to learn the probability density function (PDF) of continuous context variable online. The first algorithm is simpler, which directly optimizes the expectation under the estimated PDF. Considering that the estimated PDF may have high estimation error when the true distribution is complicated, we further propose the second algorithm that optimizes the distributionally robust objective. Theoretical results demonstrate that both algorithms have sub-linear Bayesian cumulative regret on the expectation objective. Furthermore, we conduct numerical experiments to empirically demonstrate the effectiveness of our algorithms.
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We propose to estimate the weight matrix used for forecast reconciliation as parameters in a general linear model in order to quantify its uncertainty. This implies that forecast reconciliation can be formulated as an orthogonal projection from the space of base-forecast errors into a coherent linear subspace. We use variance decomposition together with the Wishart distribution to derive the central estimator for the forecast-error covariance matrix. In addition, we prove that distance-reducing properties apply to the reconciled forecasts at all levels of the hierarchy as well as to the forecast-error covariance. A covariance matrix for the reconciliation weight matrix is derived, which leads to improved estimates of the forecast-error covariance matrix. We show how shrinkage can be introduced in the formulated model by imposing specific priors on the weight matrix and the forecast-error covariance matrix. The method is illustrated in a simulation study that shows consistent improvements in the log-score. Finally, standard errors for the weight matrix and the variance-separation formula are illustrated using a case study of forecasting electricity load in Sweden.
Efficiently generating statistically independent samples from an unnormalized probability distribution, such as equilibrium samples of many-body systems, is a foundational problem in science. In this paper, we propose Iterated Denoising Energy Matching (iDEM), an iterative algorithm that uses a novel stochastic score matching objective leveraging solely the energy function and its gradient -- and no data samples -- to train a diffusion-based sampler. Specifically, iDEM alternates between (I) sampling regions of high model density from a diffusion-based sampler and (II) using these samples in our stochastic matching objective to further improve the sampler. iDEM is scalable to high dimensions as the inner matching objective, is simulation-free, and requires no MCMC samples. Moreover, by leveraging the fast mode mixing behavior of diffusion, iDEM smooths out the energy landscape enabling efficient exploration and learning of an amortized sampler. We evaluate iDEM on a suite of tasks ranging from standard synthetic energy functions to invariant $n$-body particle systems. We show that the proposed approach achieves state-of-the-art performance on all metrics and trains $2-5\times$ faster, which allows it to be the first method to train using energy on the challenging $55$-particle Lennard-Jones system.
In this paper, a general framework for linear secure distributed matrix multiplication (SDMM) is introduced. The model allows for a neat treatment of straggling and Byzantine servers via a star product interpretation as well as simplified security proofs. Known properties of star products also immediately yield a lower bound for the recovery threshold as well as an upper bound for the number of colluding workers the system can tolerate. Another bound on the recovery threshold is given by the decodability condition, which generalizes a bound for GASP codes. The framework produces many of the known SDMM schemes as special cases, thereby providing unification for the previous literature on the topic. Furthermore, error behavior specific to SDMM is discussed and interleaved codes are proposed as a suitable means for efficient error correction in the proposed model. Analysis of the error correction capability under natural assumptions about the error distribution is also provided, largely based on well-known results on interleaved codes. Error detection and other error distributions are also discussed.
The synthesis problem asks to automatically generate, if it exists, an algorithm from a specification of correct input-output pairs. In this paper, we consider the synthesis of computable functions of infinite words, for a classical Turing computability notion over infinite inputs. We consider specifications which are rational relations of infinite words, i.e., specifications defined non-deterministic parity transducers. We prove that the synthesis problem of computable functions from rational specifications is undecidable. We provide an incomplete but sound reduction to some parity game, such that if Eve wins the game, then the rational specification is realizable by a computable function. We prove that this function is even computable by a deterministic two-way transducer. We provide a sufficient condition under which the latter game reduction is complete. This entails the decidability of the synthesis problem of computable functions, which we prove to be ExpTime-complete, for a large subclass of rational specifications, namely deterministic rational specifications. This subclass contains the class of automatic relations over infinite words, a yardstick in reactive synthesis.
We propose a functional accelerated failure time model to characterize effects of both functional and scalar covariates on the time to event of interest, and provide regularity conditions to guarantee model identifiability. For efficient estimation of model parameters, we develop a sieve maximum likelihood approach where parametric and nonparametric coefficients are bundled with an unknown baseline hazard function in the likelihood function. Not only do the bundled parameters cause immense numerical difficulties, but they also result in new challenges in theoretical development. By developing a general theoretical framework, we overcome the challenges arising from the bundled parameters and derive the convergence rate of the proposed estimator. Furthermore, we prove that the finite-dimensional estimator is $\sqrt{n}$-consistent, asymptotically normal and achieves the semiparametric information bound. The proposed inference procedures are evaluated by extensive simulation studies and illustrated with an application to the sequential organ failure assessment data from the Improving Care of Acute Lung Injury Patients study.
We consider causal mediation analysis with confounders subject to nonignorable missingness in a nonparametric framework. Our approach relies on shadow variables that are associated with the missing confounders but independent of the missingness mechanism. The mediation effect of interest is shown to be a weighted average of an iterated conditional expectation, which motivates our Sieve-based Iterative Outward (SIO) estimator. We derive the rate of convergence and asymptotic normality of the SIO estimator, which do not suffer from the ill-posed inverse problem. Essentially, we show that the asymptotic normality is not affected by the slow convergence rate of nonparametric estimators of nuisance functions. Moreover, we demonstrate that our estimator is locally efficient and attains the semiparametric efficiency bound under certain conditions. We accurately depict the efficiency loss attributable to missingness and identify scenarios in which efficiency loss is absent. We also propose a stable and easy-to-implement approach to estimate asymptotic variance and construct confidence intervals for the mediation effects. Finally, we evaluate the finite-sample performance of our proposed approach through simulation studies, and apply it to the CFPS data to show its practical applicability.
Several microring resonator (MRR) based analog photonic architectures have been proposed to accelerate general matrix-matrix multiplications (GEMMs) in deep neural networks with exceptional throughput and energy efficiency. To implement GEMM functions, these MRR-based architectures, in general, manipulate optical signals in five different ways: (i) Splitting (copying) of multiple optical signals to achieve a certain fan-out, (ii) Aggregation (multiplexing) of multiple optical signals to achieve a certain fan-in, (iii) Modulation of optical signals to imprint input values onto analog signal amplitude, (iv) Weighting of modulated optical signals to achieve analog input-weight multiplication, (v) Summation of optical signals. The MRR-based GEMM accelerators undertake the first four ways of signal manipulation in an arbitrary order ignoring the possible impact of the order of these manipulations on their performance. In this paper, we conduct a detailed analysis of accelerator organizations with three different orders of these manipulations: (1) Modulation-Aggregation-Splitting-Weighting (MASW), (2) Aggregation-Splitting-Modulation-Weighting (ASMW), and (3) Splitting-Modulation-Weighting-Aggregation (SMWA). We show that these organizations affect the crosstalk noise and optical signal losses in different magnitudes, which renders these organizations with different levels of processing parallelism at the circuit level, and different magnitudes of throughput and energy-area efficiency at the system level. Our evaluation results for four CNN models show that SMWA organization achieves up to 4.4$\times$, 5$\times$, and 5.2$\times$ better throughput, energy efficiency, and area-energy efficiency, respectively, compared to ASMW and MASW organizations on average.
A Differentiable Partially Observable Generalized Linear Model with Forward-Backward Message Passing
The partially observable generalized linear model (POGLM) is a powerful tool for understanding neural connectivity under the assumption of existing hidden neurons. With spike trains only recorded from visible neurons, existing works use variational inference to learn POGLM meanwhile presenting the difficulty of learning this latent variable model. There are two main issues: (1) the sampled Poisson hidden spike count hinders the use of the pathwise gradient estimator in VI; and (2) the existing design of the variational model is neither expressive nor time-efficient, which further affects the performance. For (1), we propose a new differentiable POGLM, which enables the pathwise gradient estimator, better than the score function gradient estimator used in existing works. For (2), we propose the forward-backward message-passing sampling scheme for the variational model. Comprehensive experiments show that our differentiable POGLMs with our forward-backward message passing produce a better performance on one synthetic and two real-world datasets. Furthermore, our new method yields more interpretable parameters, underscoring its significance in neuroscience.
Controllable layout generation refers to the process of creating a plausible visual arrangement of elements within a graphic design (e.g., document and web designs) with constraints representing design intentions. Although recent diffusion-based models have achieved state-of-the-art FID scores, they tend to exhibit more pronounced misalignment compared to earlier transformer-based models. In this work, we propose the $\textbf{LA}$yout $\textbf{C}$onstraint diffusion mod$\textbf{E}$l (LACE), a unified model to handle a broad range of layout generation tasks, such as arranging elements with specified attributes and refining or completing a coarse layout design. The model is based on continuous diffusion models. Compared with existing methods that use discrete diffusion models, continuous state-space design can enable the incorporation of differentiable aesthetic constraint functions in training. For conditional generation, we introduce conditions via masked input. Extensive experiment results show that LACE produces high-quality layouts and outperforms existing state-of-the-art baselines.
In LiDAR-based 3D object detection for autonomous driving, the ratio of the object size to input scene size is significantly smaller compared to 2D detection cases. Overlooking this difference, many 3D detectors directly follow the common practice of 2D detectors, which downsample the feature maps even after quantizing the point clouds. In this paper, we start by rethinking how such multi-stride stereotype affects the LiDAR-based 3D object detectors. Our experiments point out that the downsampling operations bring few advantages, and lead to inevitable information loss. To remedy this issue, we propose Single-stride Sparse Transformer (SST) to maintain the original resolution from the beginning to the end of the network. Armed with transformers, our method addresses the problem of insufficient receptive field in single-stride architectures. It also cooperates well with the sparsity of point clouds and naturally avoids expensive computation. Eventually, our SST achieves state-of-the-art results on the large scale Waymo Open Dataset. It is worth mentioning that our method can achieve exciting performance (83.8 LEVEL 1 AP on validation split) on small object (pedestrian) detection due to the characteristic of single stride. Codes will be released at //github.com/TuSimple/SST
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