The boosted Frank-Wolfe algorithm accelerates the classical Frank-Wolfe algorithm by better aligning the update direction with the negative gradient. Its analysis, however, has been limited to deterministic convex problems, with step sizes that require either line search or knowledge of the Lipschitz constant of the gradient. We develop a novel step size strategy that does not depend on the Lipschitz constant of the gradient, which allows us to extend the boosted Frank-Wolfe algorithm to the stochastic setting. We prove that boosting with this step size strategy can be combined with many modern gradient estimators, including SAGA, L-SVRG, SAG, Heavy Ball momentum, and zeroth-order estimators, among others, while retaining the worst-case convergence rates of ordinary stochastic Frank-Wolfe. Our analysis also yields the first convergence rates for boosted Frank-Wolfe on nonconvex and quasar-convex objectives, results which are new even for deterministic problems. Experiments on sparse logistic regression and quantum process tomography show that stochastic boosted Frank-Wolfe achieves faster convergence per gradient oracle call (and on wall-clock) compared to the non-boosted baseline.
In this paper we obtain an approximate solution of Einstein field equations which describes a general boosted Kerr-Newman black hole relative to a Lorentz frame at future null infinity. The boosted black hole is obtained from a general twisting metric whose boost emerges from the BMS group. Employing a standard procedure we build the electromagnetic energy-momentum tensor with the Kerr boosted metric together with its timelike Killing vector as the electromagnetic potential. We demonstrate that our solution satisfies Einstein field equations up to a fourth-order expansion in $1/r$, indicating that the spacetime closely resembles a Kerr-Newman black hole whose boost points in a arbitrary direction. Spacetime structures of the general black hole -- namely the event horizon and ergosphere -- are examined in Bondi-Sachs coordinates. For a proper timelike observer we show that the electric field generated by the boosted black hole exhibits a purely radial behavior, whereas the magnetic field develops a complex structure characterized by two pronounced lobes oriented opposite to the boost direction.
In this paper we obtain a new solution of Einstein field equations which describes a boosted Kerr-Newman black hole relative to a Lorentz frame at future null infinity. To simplify our analysis we consider a particular configuration in which the boost is aligned with the black hole angular momentum. The boosted Kerr-Newman black hole is obtained considering the complete asymptotic Lorentz transformations of Robinson-Trautman coordinates to Bondi-Sachs, including the perturbation term of the boosted Robinson-Trautman metric. To verify that the final form of the metric is indeed a solution of Einstein field equations, we evaluate the corresponding energy-momentum tensor the boosted Kerr-Newman solution. To this end, we consider the electromagnetic energy-momentum tensor built with the Kerr boosted metric together with its timelike killing vector. We show that the Papapetrou field thus obtained engender an energy-momentum tensor which satisfies Einstein field equations up to 4th order for the Kerr-Newman metric. To proceed, we examine the causal structure of the boosted Kerr-Newman black hole in Bondi-Sachs coordinates as in a preferred timelike foliation. We show that the ultimate ef
Energetic cosmic rays scatter off the cosmic neutrino background throughout the history of the Universe, yielding a diffuse flux of cosmic relic neutrinos boosted to high energies. We calculate this flux under different assumptions of the cosmic-ray flux spectral slope and redshift evolution. The non-observation of the diffuse flux of boosted relic neutrinos with current high-energy neutrino experiments already excludes an average cosmic neutrino background overdensity larger than $\sim 10^{4}$ over cosmological distances. We discuss the future detectability of the diffuse flux of boosted relic neutrinos in light of neutrino overdensity estimates and cosmogenic neutrino backgrounds.
Gradient boosted decision trees have achieved remarkable success in several domains, particularly those that work with static tabular data. However, the application of gradient boosted models to signal processing is underexplored. In this work, we introduce gradient boosted filters for dynamic data, by employing Hammerstein systems in place of decision trees. We discuss the relationship of our approach to the Volterra series, providing the theoretical underpinning for its application. We demonstrate the effective generalizability of our approach with examples.
Dark matter can be boosted by high energy particles in astrophysical environments through elastic scattering. We study the production of boosted dark matter via scattering with electrons in the relativistic jet of the closest active galactic nucleus, Centaurus A, and its detection in the Super-Kamiokande experiment. Since there are a huge number of electrons in the jet and dark matter is extremely dense around the supermassive black hole that powers the jet, the number of boosted dark matter is tremendously large. Compared to boosted dark matter from blazars, the dark matter flux from Centaurus A is enhanced due to the proximity of Centaurus A. The constraint on dark matter-electron scattering cross section set by Super-Kamiokande is more stringent, down to $\sim 10^{-36} \, \mathrm{cm}^2$ for $\mathrm{MeV}$ dark matter.
This paper introduces a boosted conformal procedure designed to tailor conformalized prediction intervals toward specific desired properties, such as enhanced conditional coverage or reduced interval length. We employ machine learning techniques, notably gradient boosting, to systematically improve upon a predefined conformity score function. This process is guided by carefully constructed loss functions that measure the deviation of prediction intervals from the targeted properties. The procedure operates post-training, relying solely on model predictions and without modifying the trained model (e.g., the deep network). Systematic experiments demonstrate that starting from conventional conformal methods, our boosted procedure achieves substantial improvements in reducing interval length and decreasing deviation from target conditional coverage.
We train several neural networks and boosted decision trees to discriminate fully-hadronic boosted di-$τ$ topologies against background QCD jets, using calorimeter and tracking information. Boosted di-$τ$ topologies consisting of a pair of highly collimated $τ$-leptons, arise from the decay of a highly energetic Standard Model Higgs or Z boson or from particles beyond the Standard Model. We compare the tagging performance for different neural-network models and a boosted decision tree, the latter serving as a simple benchmark machine learning model.
Combining the merits of both denoising diffusion probabilistic models and gradient boosting, the diffusion boosting paradigm is introduced for tackling supervised learning problems. We develop Diffusion Boosted Trees (DBT), which can be viewed as both a new denoising diffusion generative model parameterized by decision trees (one single tree for each diffusion timestep), and a new boosting algorithm that combines the weak learners into a strong learner of conditional distributions without making explicit parametric assumptions on their density forms. We demonstrate through experiments the advantages of DBT over deep neural network-based diffusion models as well as the competence of DBT on real-world regression tasks, and present a business application (fraud detection) of DBT for classification on tabular data with the ability of learning to defer.
In this paper we propose using the principle of boosting to reduce the bias of a random forest prediction in the regression setting. From the original random forest fit we extract the residuals and then fit another random forest to these residuals. We call the sum of these two random forests a \textit{one-step boosted forest}. We show with simulated and real data that the one-step boosted forest has a reduced bias compared to the original random forest. The paper also provides a variance estimate of the one-step boosted forest by an extension of the infinitesimal Jackknife estimator. Using this variance estimate we can construct prediction intervals for the boosted forest and we show that they have good coverage probabilities. Combining the bias reduction and the variance estimate we show that the one-step boosted forest has a significant reduction in predictive mean squared error and thus an improvement in predictive performance. When applied on datasets from the UCI database, one-step boosted forest performs better than random forest and gradient boosting machine algorithms. Theoretically we can also extend such a boosting process to more than one step and the same principles out
Boosted trees is a dominant ML model, exhibiting high accuracy. However, boosted trees are hardly intelligible, and this is a problem whenever they are used in safety-critical applications. Indeed, in such a context, rigorous explanations of the predictions made are expected. Recent work have shown how subset-minimal abductive explanations can be derived for boosted trees, using automated reasoning techniques. However, the generation of such well-founded explanations is intractable in the general case. To improve the scalability of their generation, we introduce the notion of tree-specific explanation for a boosted tree. We show that tree-specific explanations are abductive explanations that can be computed in polynomial time. We also explain how to derive a subset-minimal abductive explanation from a tree-specific explanation. Experiments on various datasets show the computational benefits of leveraging tree-specific explanations for deriving subset-minimal abductive explanations.
A muon collider could produce the heavier Standard Model particles with a boost, for example in resonant processes such as $μ^-μ^+\to h$ or $μ^-μ^+\to Z$. We propose machine configurations that produce the boost (asymmetric beam energies, tilted beams) and estimate how much the luminosity is reduced or perhaps enhanced. The feasibility of the proposed configurations, as well as an estimation of the beam-induced backgrounds and beam energy spread, needs to be evaluated in order to derive more solid conclusions on the physics potential of such boosted collider configurations. If achievable, the boost can provide new interesting observational opportunities. For example it can significantly enhance the sensitivity to long-lived new particles decaying in a far-away detector, such as dark higgses or sterile neutrinos produced in $h$ or $Z$ decays.
Boosted dark matter provides a promising approach to probe the light dark matter, whose computational framework in the spin-independent scattering process is well developed. However, the spin-dependent one lacks a unified treatment. The novelty of this paper is to give the first comprehensive derivation of the cross-section for boosted dark matter in spin-dependent scattering. When the transfer momentum is sufficiently large, there is a sizable enhancement to the proton structure factor from the time component. Besides, we find a residue momentum dependence in the quark-nucleon matching procedure, even without a light mediator. Such behavior can enhance the sensitivity compared with conventional contact interaction. We promote this endeavor by deriving direct limits on sub-GeV spin-dependent boosted dark matter through terrestrial data. The numerical results of the boosted structure factor and the non-relativistic structure factor are given explicitly in the paper and it shows that the excluded region of the boosted structure factor is about six orders larger than the non-relativistic structure factor.
The spacetime of a boosted Bondi-Sachs rotating black hole is considered as a proper background to examine electromagnetic configurations connected to analytic solutions of Maxwell equations. In our analysis, we first use the Bondi-Sachs transformations in order to bring the boosted rotating black hole metric into the Kerr-Schild form, from which zero angular momentum observers (ZAMOs) are constructed via the ADM formalism. In Kerr-Schild coordinates we obtain the Killing fields as sources of Maxwell electrodynamics, and we fix a ZAMO in order to evaluate the components of the electric and magnetic fields, from which we obtain nonsingular patterns of an eventual momentum-energy emission of a boosted Kerr-Schild black hole. Distinct patterns are examined and discussed in the case of variations of the boost parameter $γ$. We extend our analysis by considering the nonsingular electromagnetic emission in the framework of a boosted Bondi-Sachs rotating black hole, as it moves at relativistic speeds. We also discuss possible mechanisms that may resemble magnetospheres of rotating boosted black holes and give rise to hydromagnetic flows from accretion discs and to the production of jets.
We introduce a new jet shape -- N-subjettiness -- designed to identify boosted hadronically-decaying objects like electroweak bosons and top quarks. Combined with a jet invariant mass cut, N-subjettiness is an effective discriminating variable for tagging boosted objects and rejecting the background of QCD jets with large invariant mass. In efficiency studies of boosted W bosons and top quarks, we find tagging efficiencies of 30% are achievable with fake rates of 1%. We also consider the discovery potential for new heavy resonances that decay to pairs of boosted objects, and find significant improvements are possible using N-subjettiness. In this way, N-subjettiness combines the advantages of jet shapes with the discriminating power seen in previous jet substructure algorithms.
We apply the ultrarelativistic boosting procedure to map the metric of Schwarzschild-de Sitter spacetime into a metric describing de Sitter spacetime plus a shock-wave singularity located on a null hypersurface, by exploiting the picture of the embedding of an hyperboloid in a five-dimensional Minkowski spacetime. After reverting to the usual four-dimensional formalism, we also solve the geodesic equation and evaluate the Riemann curvature tensor of the boosted Schwarzschild-de Sitter metric by means of numerical calculations, which make it possible to reach the ultrarelativistic regime gradually by letting the boost velocity approach the speed of light. Eventually, the analysis of the Kretschmann invariant (and of the geodesic equation) shows the global structure of space- time, as we demonstrate the presence of a "scalar curvature singularity" within a 3-sphere and find that it is also possible to define what we have called "boosted horizon", a sort of elastic wall where all particles are surprisingly pushed away. This seems to suggest that such "boosted geometries" are ruled by a sort of "antigravity effect" since all geodesics seem to refuse entering the "boosted horizon" and a
In this work, we demonstrate the advantage of the pGMM (``powered generalized min-max'') kernel in the context of (ridge) regression. In recent prior studies, the pGMM kernel has been extensively evaluated for classification tasks, for logistic regression, support vector machines, as well as deep neural networks. In this paper, we provide an experimental study on ridge regression, to compare the pGMM kernel regression with the ordinary ridge linear regression as well as the RBF kernel ridge regression. Perhaps surprisingly, even without a tuning parameter (i.e., $p=1$ for the power parameter of the pGMM kernel), the pGMM kernel already performs well. Furthermore, by tuning the parameter $p$, this (deceptively simple) pGMM kernel even performs quite comparably to boosted trees. Boosting and boosted trees are very popular in machine learning practice. For regression tasks, typically, practitioners use $L_2$ boost, i.e., for minimizing the $L_2$ loss. Sometimes for the purpose of robustness, the $L_1$ boost might be a choice. In this study, we implement $L_p$ boost for $p\geq 1$ and include it in the package of ``Fast ABC-Boost''. Perhaps also surprisingly, the best performance (in te
Contrary to a prevailing assumption that black holes would swiftly discharge, we argue that black holes can charge preferentially when boosted through an ambient magnetic field. Though the details are very different, the preference for charge is related to the precipitation of the Wald charge on a spinning black hole in an ambient magnetic field. The gravito-electrodynamics upstage naive arguments about screening electric fields in determining the value of the charge accrued. Charged test particles, which build up the black hole charge, exhibit chaotic behavior as evidenced by fractal basin boundaries between dynamical regions. Charged, boosted black holes will generate their own electromagnetic fields and thereby their own luminous signatures, even if they are initially bare. We therefore add boosted black holes to the growing list of potentially observable black hole signatures, alongside black hole batteries and black hole pulsars. The implications should be relevant for supermassive black holes that are boosted relative to a galactic magnetic field as well as black holes merging with magnetized neutron stars.
The ultrarelativistic boosting procedure had been applied in the literature to map the metric of Schwarzschild-de Sitter spacetime into a metric describing de Sitter spacetime plus a shock-wave singularity located on a null hypersurface. This paper evaluates the Riemann curvature tensor of the boosted Schwarzschild-de Sitter metric by means of numerical calculations, which make it possible to reach the ultrarelativistic regime gradually by letting the boost velocity approach the speed of light. Thus, for the first time in the literature, the singular limit of curvature through Dirac's delta distribution and its derivatives is numerically evaluated for this class of spacetimes. Eventually, the analysis of the Kretschmann invariant and the geodesic equation show that the spacetime possesses a scalar curvature singularity within a 3-sphere and it is possible to define what we here call boosted horizon, a sort of elastic wall where all particles are surprisingly pushed away, as numerical analysis demonstrates. This seems to suggest that boosted geometries are ruled by a sort of antigravity effect since all geodesics seem to refuse to enter the boosted horizon, even though their initial
Gradient boosted decision trees are a popular machine learning technique, in part because of their ability to give good accuracy with small models. We describe two extensions to the standard tree boosting algorithm designed to increase this advantage. The first improvement extends the boosting formalism from scalar-valued trees to vector-valued trees. This allows individual trees to be used as multiclass classifiers, rather than requiring one tree per class, and drastically reduces the model size required for multiclass problems. We also show that some other popular vector-valued gradient boosted trees modifications fit into this formulation and can be easily obtained in our implementation. The second extension, layer-by-layer boosting, takes smaller steps in function space, which is empirically shown to lead to a faster convergence and to a more compact ensemble. We have added both improvements to the open-source TensorFlow Boosted trees (TFBT) package, and we demonstrate their efficacy on a variety of multiclass datasets. We expect these extensions will be of particular interest to boosted tree applications that require small models, such as embedded devices, applications requiri