We developed a statistical inference method applicable to a broad range of generalized linear models (GLMs) in high-dimensional settings, where the number of unknown coefficients scales proportionally with the sample size. Although a pioneering inference method has been developed for logistic regression, which is a specific instance of GLMs, it is not feasible to apply this method directly to other GLMs because of unknown hyper-parameters. In this study, we addressed this limitation by developing a new inference method designed for a certain class of GLMs. Our method is based on the adjustment of asymptotic normality in high dimensions and is feasible in the sense that it is possible even with unknown hyper-parameters. Specifically, we introduce a novel convex loss-based estimator and its associated system, which are essential components of inference. Next, we devise a methodology for identifying the system parameters required by the method. Consequently, we construct confidence intervals for GLMs in a high-dimensional regime. We prove that our proposed method has desirable theoretical properties, such as strong consistency and exact coverage probability. Finally, we experimentally confirmed its validity.
相關內容
Cosmological simulations play a crucial role in elucidating the effect of physical parameters on the statistics of fields and on constraining parameters given information on density fields. We leverage diffusion generative models to address two tasks of importance to cosmology -- as an emulator for cold dark matter density fields conditional on input cosmological parameters $\Omega_m$ and $\sigma_8$, and as a parameter inference model that can return constraints on the cosmological parameters of an input field. We show that the model is able to generate fields with power spectra that are consistent with those of the simulated target distribution, and capture the subtle effect of each parameter on modulations in the power spectrum. We additionally explore their utility as parameter inference models and find that we can obtain tight constraints on cosmological parameters.
Morphing quadrotors with four external actuators can adapt to different restricted scenarios by changing their geometric structure. However, previous works mainly focus on the improvements in structures and controllers, and existing planning algorithms don't consider the morphological modifications, which leads to safety and dynamic feasibility issues. In this paper, we propose a unified planning and control framework for morphing quadrotors to deform autonomously and efficiently. The framework consists of a milliseconds-level spatial-temporal trajectory optimizer that takes into account the morphological modifications of quadrotors. The optimizer can generate full-body safety trajectories including position and attitude. Additionally, it incorporates a nonlinear attitude controller that accounts for aerodynamic drag and dynamically adjusts dynamic parameters such as the inertia tensor and Center of Gravity. The controller can also online compute the thrust coefficient during morphing. Benchmark experiments compared with existing methods validate the robustness of the proposed controller. Extensive simulations and real-world experiments are performed to demonstrate the effectiveness of the proposed framework.
Transformer neural networks can exhibit a surprising capacity for in-context learning (ICL) despite not being explicitly trained for it. Prior work has provided a deeper understanding of how ICL emerges in transformers, e.g. through the lens of mechanistic interpretability, Bayesian inference, or by examining the distributional properties of training data. However, in each of these cases, ICL is treated largely as a persistent phenomenon; namely, once ICL emerges, it is assumed to persist asymptotically. Here, we show that the emergence of ICL during transformer training is, in fact, often transient. We train transformers on synthetic data designed so that both ICL and in-weights learning (IWL) strategies can lead to correct predictions. We find that ICL first emerges, then disappears and gives way to IWL, all while the training loss decreases, indicating an asymptotic preference for IWL. The transient nature of ICL is observed in transformers across a range of model sizes and datasets, raising the question of how much to "overtrain" transformers when seeking compact, cheaper-to-run models. We find that L2 regularization may offer a path to more persistent ICL that removes the need for early stopping based on ICL-style validation tasks. Finally, we present initial evidence that ICL transience may be caused by competition between ICL and IWL circuits.
The purpose of this work is to present an effective tool for computing different QR-decompositions of a complex nonsingular square matrix. The concept of the discrete signal-induced heap transform (DsiHT, Grigoryan 2006) is used. This transform is fast, has a unique algorithm for any length of the input vector/signal and can be used with different complex basic 2x2 transforms. The DsiHT zeroes all components of the input signal while moving or heaping the energy of the signal into one component, such as the first. We describe three different types of QR-decompositions that use the basic transforms with the T, G, and M-type complex matrices we introduce, and also without matrices, but using analytical formulas. We also present the mixed QR-decomposition, when different type DsiHTs are used at different stages of the algorithm. The number of such decompositions is greater than 3^((N-1)), for an NxN complex matrix. Examples of the QR-decomposition are described in detail for the 4x4 and 6x6 complex matrices and compared with the known method of Householder transforms. The precision of the QR-decompositions of NxN matrices, when N are 6, 13, 17, 19, 21, 40, 64, 100, 128, 201, 256, and 400 is also compared. The MATLAB-based scripts of the codes for QR-decompositions by the described DsiHTs are given.
Nonparametric estimates of frequency response functions (FRFs) are often suitable for describing the dynamics of a mechanical system. If treating these estimates as measurement inputs, they can be used for parametric identification of, e.g., a gray-box model. Classical methods for nonparametric FRF estimation of MIMO systems require at least as many experiments as the system has inputs. Local parametric FRF estimation methods have been developed for avoiding multiple experiments. In this paper, these local methods are adapted and applied for estimating the FRFs of a 6-axes robotic manipulator, which is a nonlinear MIMO system operating in closed loop. The aim is to reduce the experiment time and amount of data needed for identification. The resulting FRFs are analyzed in an experimental study and compared to estimates obtained by classical MIMO techniques. It is furthermore shown that an accurate parametric model identification is possible based on local parametric FRF estimates and that the total experiment time can be significantly reduced.
Valued constraint satisfaction problems (VCSPs) are a large class of computational optimisation problems. If the variables of a VCSP take values from a finite domain, then recent results in constraint satisfaction imply that the problem is in P or NP-complete, depending on the set of admitted cost functions. Here we study the larger class of cost functions over countably infinite domains that have an oligomorphic automorphism group. We present a hardness condition based on a generalisation of pp-constructability as known for (classical) CSPs. We also provide a universal-algebraic polynomial-time tractability condition, based on the concept of fractional polymorphisms. We apply our general theory to study the computational complexity of resilience problems in database theory (under bag semantics). We show how to construct, for every fixed conjunctive query (and more generally for every union of conjunctive queries), a set of cost functions with an oligomorphic automorphism group such that the resulting VCSP is polynomial-time equivalent to the resilience problem; we only require that the query is connected and show that this assumption can be made without loss of generality. For the case where the query is acylic, we obtain a complexity dichotomy of the resilience problem, based on the dichotomy for finite-domain VCSPs. To illustrate the utility of our methods, we exemplarily settle the complexity of a (non-acyclic) conjunctive query whose computational complexity remained open in the literature by verifying that it satisfies our tractability condition. We conjecture that for resilience problems, our hardness and tractability conditions match, which would establish a complexity dichotomy for resilience problems for (unions of) conjunctive queries.
Autonomous vehicles (AVs) fuse data from multiple sensors and sensing modalities to impart a measure of robustness when operating in adverse conditions. Radars and cameras are popular choices for use in sensor fusion; although radar measurements are sparse in comparison to camera images, radar scans penetrate fog, rain, and snow. However, accurate sensor fusion depends upon knowledge of the spatial transform between the sensors and any temporal misalignment that exists in their measurement times. During the life cycle of an AV, these calibration parameters may change, so the ability to perform in-situ spatiotemporal calibration is essential to ensure reliable long-term operation. State-of-the-art 3D radar-camera spatiotemporal calibration algorithms require bespoke calibration targets that are not readily available in the field. In this paper, we describe an algorithm for targetless spatiotemporal calibration that does not require specialized infrastructure. Our approach leverages the ability of the radar unit to measure its own ego-velocity relative to a fixed, external reference frame. We analyze the identifiability of the spatiotemporal calibration problem and determine the motions necessary for calibration. Through a series of simulation studies, we characterize the sensitivity of our algorithm to measurement noise. Finally, we demonstrate accurate calibration for three real-world systems, including a handheld sensor rig and a vehicle-mounted sensor array. Our results show that we are able to match the performance of an existing, target-based method, while calibrating in arbitrary, infrastructure-free environments.
Topology identification (TI) is a key task for state estimation (SE) in distribution grids, especially the one with high-penetration renewables. The uncertainties, initiated by the time-series behavior of renewables, will almost certainly lead to bad TI results without a proper treatment. These uncertainties are analytically intractable under conventional framework-they are usually jointly spatial-temporal dependent, and hence cannot be simply treated as white noise. For this purpose, a hybrid framework is suggested in this paper to handle these uncertainties in a systematic and theoretical way; in particular, big data analytics are studied to harness the jointly spatial-temporal statistical properties of those uncertainties. With some prior knowledge, a model bank is built first to store the countable typical models of network configurations; therefore, the difference between the SE outputs of each bank model and our observation is capable of being defined as a matrix variate-the so-called random matrix. In order to gain insight into the random matrix, a well-designed metric space is needed. Auto-regression (AR) model, factor analysis (FA), and random matrix theory (RMT) are tied together for the metric space design, followed by jointly temporal-spatial analysis of those matrices which is conducted in a high-dimensional (vector) space. Under the proposed framework, some big data analytics and theoretical results are obtained to improve the TI performance. Our framework is validated using IEEE standard distribution network with some field data in practice.
In causal inference, it is a fundamental task to estimate the causal effect from observational data. However, latent confounders pose major challenges in causal inference in observational data, for example, confounding bias and M-bias. Recent data-driven causal effect estimators tackle the confounding bias problem via balanced representation learning, but assume no M-bias in the system, thus they fail to handle the M-bias. In this paper, we identify a challenging and unsolved problem caused by a variable that leads to confounding bias and M-bias simultaneously. To address this problem with co-occurring M-bias and confounding bias, we propose a novel Disentangled Latent Representation learning framework for learning latent representations from proxy variables for unbiased Causal effect Estimation (DLRCE) from observational data. Specifically, DLRCE learns three sets of latent representations from the measured proxy variables to adjust for the confounding bias and M-bias. Extensive experiments on both synthetic and three real-world datasets demonstrate that DLRCE significantly outperforms the state-of-the-art estimators in the case of the presence of both confounding bias and M-bias.
The extremely large-scale massive multiple-input multiple-output (XL-MIMO) has the potential to achieve boosted spectral efficiency and refined spatial resolution for future wireless networks. However, channel estimation for XL-MIMO is challenging since the large number of antennas results in high computational complexity with the near-field effect. In this letter, we propose a low-complexity sequential angle-distance channel estimation (SADCE) method for near-field XL-MIMO systems equipped with uniformly planar arrays (UPA). Specifically, we first successfully decouple the angle and distance parameters, which allows us to devise a two-dimensional discrete Fourier transform (2D-DFT) method for angle parameters estimation. Then, a low-complexity distance estimation method is proposed with a closed-form solution. Compared with existing methods, the proposed method achieves significant performance gain with noticeably reduced computational complexity.Numerical results verify the superiority of the proposed near-field channel estimation algorithm.
注冊地址： 北京市海淀區羊坊店路18號2幢3層301-191