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Type II supernovae (SNeII) mark the endpoint in the lives of hydrogen-rich massive stars. Their large explosion energies and luminosities allow us to measure distances, metallicities, and star formation rates into the distant Universe. To fully exploit their use in answering different astrophysical problems, high-quality low-redshift data sets are required. Such samples are vital to understand the physics of SNeII, but also to serve as calibrators for distinct - and often lower-quality - samples. We present uBgVri optical and YJH near-infrared (NIR) photometry for 94 low-redshift SNeII observed by the Carnegie Supernova Project (CSP). A total of 9817 optical and 1872 NIR photometric data points are released, leading to a sample of high-quality SNII light curves during the first ~150 days post explosion on a well-calibrated photometric system. The sample is presented and its properties are analysed and discussed through comparison to literature events. We also focus on individual SNeII as examples of classically defined subtypes and outlier objects. Making a cut in the plateau decline rate of our sample (s2), a new subsample of fast-declining SNeII is presented. The sample has a median redshift of 0.015, with the nearest event at 0.001 and the most distant at 0.07. At optical wavelengths (V), the sample has a median cadence of 4.7 days over the course of a median coverage of 80 days. In the NIR (J), the median cadence is 7.2 days over the course of 59 days. The fast-declining subsample is more luminous than the full sample and shows shorter plateau phases. Of the non-standard SNeII highlighted, SN2009A particularly stands out with a steeply declining then rising light curve, together with what appears to be two superimposed P-Cygni profiles of H-alpha in its spectra. We outline the significant utility of these data, and finally provide an outlook of future SNII science., Comment: Accepted for publication in A&A. Photometric data will be uploaded to the CDS and the CSP website, and can also be requested from the first author

Scalar field comparison is a fundamental task in scientific visualization. In topological data analysis, we compare topological descriptors of scalar fields -- such as persistence diagrams and merge trees -- because they provide succinct and robust abstract representations. Several similarity measures for topological descriptors seem to be both asymptotically and practically efficient with polynomial time algorithms, but they do not scale well when handling large-scale, time-varying scientific data and ensembles. In this paper, we propose a new framework to facilitate the comparative analysis of merge trees, inspired by tools from locality sensitive hashing (LSH). LSH hashes similar objects into the same hash buckets with high probability. We propose two new similarity measures for merge trees that can be computed via LSH, using new extensions to Recursive MinHash and subpath signature, respectively. Our similarity measures are extremely efficient to compute and closely resemble the results of existing measures such as merge tree edit distance or geometric interleaving distance. Our experiments demonstrate the utility of our LSH framework in applications such as shape matching, clustering, key event detection, and ensemble summarization., Comment: IEEE VIS 2024

The origin of strong sodium absorption, which has been observed for a few nearby Type Ia supernovae (SNe Ia), remains elusive. Here we analyse two high-signal-to-noise, intermediate-resolution VLT/X-shooter spectra at epochs $+$18 and $+$27 days past peak brightness of the strongly lensed and multiply-imaged Type Ia SN 2016geu which exploded at a redshift of $z = 0.4$. We show that SN 2016geu exhibits very strong, multiple Na I and Ca II absorption lines with a large total Na I D restframe equivalent width of 5.2 $\pm$ 0.2 A, among the highest ever detected for a SN Ia and similar to only a handful of nearby SNe Ia with extraordinary large Na I D EWs. The absorption system is time-invariant and extends over a large velocity span $\sim$ 250 km s$^{-1}$. The majority of the absorption is blueshifted relative to the strongest component, while there are both blueshifted and redshifted components relative to the systemic redshift of the galaxy. The column density ratios and widths of the absorption lines indicate that the absorption likely arises from a combination of interstellar dusty molecular clouds and circumgalactic in- and outflowing material, rather than circumstellar matter around the SN., Comment: 12 pages, 6 figures, accepted for publication in ApJ

Understanding the nature of the luminous 1991T-like supernovae is of great importance to supernova cosmology as they are likely to have been more common in the early universe. In this paper we explore the observational properties of 1991T-like supernovae to study their relationship to other luminous, slow-declining Type~Ia supernovae (SNe Ia). From the spectroscopic and photometric criteria defined in Phillips et al. (1992), we identify 17 1991T-like supernovae from the literature. Combining these objects with ten 1991T-like supernovae from the Carnegie Supernova Project-II, the spectra, light curves, and colors of these events, along with their host galaxy properties, are examined in detail. We conclude that 1991T-like supernovae are closely related in essentially all of their UV, optical, and near-infrared properties -- as well as their host galaxy parameters -- to the slow-declining subset of Branch core-normal supernovae and to the intermediate 1999aa-like events, forming a continuum of luminous SNe Ia. The overriding difference between these three subgroups appears to be the extent to which $^{56}$Ni mixes into the ejecta, producing the pre-maximum spectra dominated by Fe III absorption, the broader UV light curves, and the higher luminosities that characterize the 1991T-like events. Nevertheless, the association of 1991T-like SNe with the rare Type Ia CSM supernovae would seem to run counter to this hypothesis, in which case 1991T-like events may form a separate subclass of SNe Ia, possibly arising from single-degenerate progenitor systems., Comment: Accepted for publication in ApJS

We present the second and final release of optical spectroscopy of Type Ia Supernovae (SNe Ia) obtained during the first and second phases of the Carnegie Supernova Project (CSP-I and CSP-II). The newly released data consist of 148 spectra of 30 SNe Ia observed in the course of the CSP-I, and 234 spectra of 127 SNe Ia obtained during the CSP-II. We also present 216 optical spectra of 46 historical SNe Ia, including 53 spectra of 30 SNe Ia observed by the Cal\'an/Tololo Supernova Survey. We combine these observations with previously published CSP data and publicly-available spectra to compile a large sample of measurements of spectroscopic parameters at maximum light, consisting of pseudo-equivalent widths and expansion velocities of selected features, for 232 CSP and historical SNe Ia (including more than 1000 spectra). Finally, we review some of the strongest correlations between spectroscopic and photometric properties of SNe Ia. Specifically, we define two samples: one consisting of SNe Ia discovered by targeted searches (most of them CSP-I objects) and the other composed of SNe Ia discovered by untargeted searches, which includes most of the CSP-II objects. The analysed correlations are similar for both samples. We find a larger incidence of SNe Ia belonging to the Cool (CL)and Broad Line (BL) Branch subtypes among the events discovered by targeted searches, Shallow Silicon (SS) SNe Ia are present with similar frequencies in both samples, while Core Normal (CN) SNe Ia are more frequent in untargeted searches., Comment: 59 pages, 16 figures, accepted for publication in The Astrophysical Journal. May 7, 2024: LaTex file updated: corrected one missing comma and an extraneous space in Table 2

We present a JWST MIRI/MRS spectrum (5-27 $\mathrm{\mu}$m) of the Type Ia supernova (SN Ia), SN 2021aefx at $+415$ days past $B$-band maximum. The spectrum, which was obtained during the iron-dominated nebular phase, has been analyzed in combination with previous JWST observations of SN 2021aefx, to provide the first JWST time series analysis of an SN Ia. We find the temporal evolution of the [Co III] 11.888 $\mathrm{\mu}$m feature directly traces the decay of $^{56}$Co. The spectra, line profiles, and their evolution are analyzed with off-center delayed-detonation models. Best fits were obtained with White Dwarf (WD) central densities of $\rho_c=0.9-1.1\times 10^9$g cm$^{-3}$, a WD mass of M$_{\mathrm{WD}}$=1.33-1.35M$_\odot$, a WD magnetic field of $\approx10^6$G, and an off-center deflagration-to-detonation transition at $\approx$ 0.5 $M_\odot$ seen opposite to the line of sight of the observer (-30). The inner electron capture core is dominated by energy deposition from $\gamma$-rays whereas a broader region is dominated by positron deposition, placing SN 2021aefx at +415 d in the transitional phase of the evolution to the positron-dominated regime. The formerly `flat-tilted' profile at 9 $\mathrm{\mu}$m now has significant contribution from [Ni IV], [Fe II], and [Fe III] and less from [Ar III], which alters the shape of the feature as positrons excite mostly the low-velocity Ar. Overall, the strength of the stable Ni features in the spectrum is dominated by positron transport rather than the Ni mass. Based on multi-dimensional models, our analysis is consistent with a single-spot, close-to-central ignition with an indication for a pre-existing turbulent velocity field, and excludes a multiple-spot, off-center ignition., Comment: Accepted for publication in ApJ

We present a method of extrapolating the spectroscopic behavior of Type Ia supernovae (SNe Ia) in the near-infrared (NIR) wavelength regime up to 2.30 $\mu$m using optical spectroscopy. Such a process is useful for accurately estimating K-corrections and other photometric quantities of SNe Ia in the NIR. Principal component analysis is performed on data consisting of Carnegie Supernova Project I & II optical and near-infrared FIRE spectra to produce models capable of making these extrapolations. This method differs from previous spectral template methods by not parameterizing models strictly by photometric light-curve properties of SNe Ia, allowing for more flexibility of the resulting extrapolated NIR flux. A difference of around -3.1% to -2.7% in the total integrated NIR flux between these extrapolations and the observations is seen here for most test cases including Branch core-normal and shallow-silicon subtypes. However, larger deviations from the observation are found for other tests, likely due to the limited high-velocity and broad-line SNe Ia in the training sample. Maximum-light principal components are shown to allow for spectroscopic predictions of the color-stretch light-curve parameter, $s_{BV}$, within approximately $\pm$0.1 units of the value measured with photometry. We also show these results compare well with NIR templates, although in most cases the templates are marginally more fitting to observations, illustrating a need for more concurrent optical+NIR spectroscopic observations to truly understand the diversity of SNe Ia in the NIR., Comment: 25 pages, 16 figures, ApJ, in press

We refine and generalize what is known about coresets for classification problems via the sensitivity sampling framework. Such coresets seek the smallest possible subsets of input data, so one can optimize a loss function on the coreset and ensure approximation guarantees with respect to the original data. Our analysis provides the first no dimensional coresets, so the size does not depend on the dimension. Moreover, our results are general, apply for distributional input and can use iid samples, so provide sample complexity bounds, and work for a variety of loss functions. A key tool we develop is a Radamacher complexity version of the main sensitivity sampling approach, which can be of independent interest., Comment: 42 Pages

A longstanding belief holds that Bayesian Optimization (BO) with standard Gaussian processes (GP) -- referred to as standard BO -- underperforms in high-dimensional optimization problems. While this belief seems plausible, it lacks both robust empirical evidence and theoretical justification. To address this gap, we present a systematic investigation. First, through a comprehensive evaluation across eleven widely used benchmarks, we found that while the popular Square Exponential (SE) kernel often leads to poor performance, using Matern kernels enables standard BO to consistently achieve top-tier results, frequently surpassing methods specifically designed for high-dimensional optimization. Second, our theoretical analysis reveals that the SE kernels failure primarily stems from improper initialization of the length-scale parameters, which are commonly used in practice but can cause gradient vanishing in training. We provide a probabilistic bound to characterize this issue, showing that Matern kernels are less susceptible and can robustly handle much higher dimensions. Third, we propose a simple robust initialization strategy that dramatically improves the performance of the SE kernel, bringing it close to state of the art methods, without requiring any additional priors or regularization. We prove another probabilistic bound that demonstrates how the gradient vanishing issue can be effectively mitigated with our method. Our findings advocate for a re-evaluation of standard BOs potential in high-dimensional settings.

We show that a constant-size constant-error coreset for polytope distance is simple to maintain under merges of coresets. However, increasing the size cannot improve the error bound significantly beyond that constant., Comment: Presented in SoCG'19 Young Researchers Forum (CG:YRF)

We present an eigenfunction method to analyze 161 visual light curves (LCs) of Type Ia supernovae (SNe Ia) obtained by the Carnegie Supernova Project to characterize their diversity and host-galaxy correlations. The eigenfunctions are based on the delayed-detonation scenario using three parameters: the LC stretch being determined by the amount of deflagration-burning governing the 56Ni production, the main-sequence mass M_MS of the progenitor white dwarf controlling the explosion energy, and its central density rho_c shifting the 56Ni distribution. Our analysis tool (SPAT) extracts the parameters from observations and projects them into physical space using their allowed ranges M_MS < 8 M_sun, rho_c < 7-8x10^9g/cc. The residuals between fits and individual LC-points are ~ 1-3% for ~ 92% of objects. We find two distinct M_MS groups corresponding to a fast (~ 40-65 Myrs) and a slow(~ 200-500 Myrs) stellar evolution. Most underluminous SNe Ia have hosts with low star formation but high M_MS, suggesting slow evolution times of the progenitor system. 91T-likes SNe show very similar LCs and high M_MS and are correlated to star formation regions, making them potentially important tracers of star formation in the early Universe out to z = 4-11. Some 6% outliers with `non-physical' parameters can be attributed to superluminous SNe Ia and subluminous SNe Ia with hosts of active star formation. For deciphering the SNe Ia diversity and high-precision SNe Ia cosmology, the importance is shown for LCs covering out to ~ 60 days past maximum. Finally, our method and results are discussed within the framework of multiple explosion scenarios, and in light of upcoming surveys., Comment: 42 pages, 22 figures, 6 tables in main text, 2 tables in appendix. This work has been published in the ApJ journal and is in partial fulfillment of the PhD thesis of the first author

Time series discords are a useful primitive for time series anomaly detection, and the matrix profile is capable of capturing discord effectively. There exist many research efforts to improve the scalability of discord discovery with respect to the length of time series. However, there is surprisingly little work focused on reducing the time complexity of matrix profile computation associated with dimensionality of a multidimensional time series. In this work, we propose a sketch for discord mining among multi-dimensional time series. After an initial pre-processing of the sketch as fast as reading the data, the discord mining has runtime independent of the dimensionality of the original data. On several real world examples from water treatment and transportation, the proposed algorithm improves the throughput by at least an order of magnitude (50X) and only has minimal impact on the quality of the approximated solution. Additionally, the proposed method can handle the dynamic addition or deletion of dimensions inconsequential overhead. This allows a data analyst to consider "what-if" scenarios in real time while exploring the data.

Dust associated with various stellar sources in galaxies at all cosmic epochs remains a controversial topic, particularly whether supernovae (SNe) play an important role in dust production. We report evidence of dust formation in the cold, dense shell behind the ejecta-circumstellar medium (CSM) interaction in the Type Ia-CSM SN 2018evt three years after the explosion, characterized by a rise in the mid-infrared (MIR) emission accompanied by an accelerated decline in the optical radiation of the SN. Such a dust-formation picture is also corroborated by the concurrent evolution of the profiles of the Ha emission line. Our model suggests enhanced CSM dust concentration at increasing distances from the SN as compared to what can be expected from the density profile of the mass loss from a steady stellar wind. By the time of the last MIR observations at day +1041, a total amount of 1.2+-0.2x10^{-2} Msun of new dust has been formed by SN 2018evt, making SN 2018evt one of the most prolific dust factories among SNe with evidence of dust formation. The unprecedented witness of the intense production procedure of dust may shed light on the perceptions of dust formation in cosmic history., Comment: Accepted by Nature Astronomy, 6 main figures, 7 extended figures, and 2 extended tables

We present a JWST mid-infrared spectrum of the under-luminous Type Ia Supernova (SN Ia) 2022xkq, obtained with the medium-resolution spectrometer on the Mid-Infrared Instrument (MIRI) $\sim130$ days post-explosion. We identify the first MIR lines beyond 14 $\mu$m in SN Ia observations. We find features unique to under-luminous SNe Ia, including: isolated emission of stable Ni, strong blends of [Ti II], and large ratios of singly ionized to doubly ionized species in both [Ar] and [Co]. Comparisons to normal-luminosity SNe Ia spectra at similar phases show a tentative trend between the width of the [Co III] 11.888 $\mu$m feature and the SN light curve shape. Using non-LTE-multi-dimensional radiation hydro simulations and the observed electron capture elements we constrain the mass of the exploding white dwarf. The best-fitting model shows that SN 2022xkq is consistent with an off-center delayed-detonation explosion of a near-Chandrasekhar mass WD (M$_{\rm ej}$ $\approx 1.37$ M$_{\odot}$) of high-central density ($\rho_c \geq 2.0\times10^{9}$ g cm$^{-3}$) seen equator on, which produced M($^{56}$Ni) $= 0.324$ M$_{\odot}$ and M($^{58}$Ni) $\geq 0.06$ M$_{\odot}$. The observed line widths are consistent with the overall abundance distribution; and the narrow stable Ni lines indicate little to no mixing in the central regions, favoring central ignition of sub-sonic carbon burning followed by an off-center DDT beginning at a single point. Additional observations may further constrain the physics revealing the presence of additional species including Cr and Mn. Our work demonstrates the power of using the full coverage of MIRI in combination with detailed modeling to elucidate the physics of SNe Ia at a level not previously possible., Comment: 31 pages, 18 figures, accepted to ApJ; updated to accepted version

A Content-based Time Series Retrieval (CTSR) system is an information retrieval system for users to interact with time series emerged from multiple domains, such as finance, healthcare, and manufacturing. For example, users seeking to learn more about the source of a time series can submit the time series as a query to the CTSR system and retrieve a list of relevant time series with associated metadata. By analyzing the retrieved metadata, users can gather more information about the source of the time series. Because the CTSR system is required to work with time series data from diverse domains, it needs a high-capacity model to effectively measure the similarity between different time series. On top of that, the model within the CTSR system has to compute the similarity scores in an efficient manner as the users interact with the system in real-time. In this paper, we propose an effective and efficient CTSR model that outperforms alternative models, while still providing reasonable inference runtimes. To demonstrate the capability of the proposed method in solving business problems, we compare it against alternative models using our in-house transaction data. Our findings reveal that the proposed model is the most suitable solution compared to others for our transaction data problem.

We present extensive ultraviolet (UV) and optical photometric and optical spectroscopic follow-up of supernova (SN)~2021gno by the "Precision Observations of Infant Supernova Explosions" (POISE) project, starting less than two days after the explosion. Given its intermediate luminosity, fast photometric evolution, and quick transition to the nebular phase with spectra dominated by [Ca~II] lines, SN~2021gno belongs to the small family of Calcium-rich transients. Moreover, it shows double-peaked light curves, a phenomenon shared with only four other Calcium-rich events. The projected distance from the center of the host galaxy is not as large as other objects in this family. The initial optical light-curve peaks coincide with a very quick decline of the UV flux, indicating a fast initial cooling phase. Through hydrodynamical modelling of the bolometric light curve and line velocity evolution, we found that the observations are compatible with the explosion of a highly-stripped massive star with an ejecta mass of $0.8\,M_\odot$ and a $^{56}$Ni mass of $0.024~M_{\odot}$. The initial cooling phase (first light curve peak) is explained by the presence of an extended circumstellar material comprising $\sim$$10^{-2}\,M_{\odot}$ with an extension of $1100\,R_{\odot}$. We discuss if hydrogen features are present in both maximum-light and nebular spectra, and its implications in terms of the proposed progenitor scenarios for Calcium-rich transients., Comment: 21 pages, 13 figures, accepted for publication in MNRAS

We present a comprehensive data set of supernova (SN) 2016adj located within the central dust lane of Centaurus A. SN 2016adj is significantly reddened and after correcting the peak apparent $B$-band magnitude ($m_B = 17.48\pm0.05$) for Milky Way reddening and our inferred host-galaxy reddening parameters (i.e., $R_{V}^{host} = 5.7\pm0.7$ and $A_{V}^{host} = 6.3\pm0.2$), we estimate it reached a peak absolute magnitude of $M_B \sim -18$. Detailed inspection of the optical/NIR spectroscopic time-series reveals a carbon-rich SN Ic and not a SN Ib/IIb as previously suggested in the literature. The NIR spectra shows prevalent carbon-monoxide formation occurring already by +41 days past $B$-band maximum, which is $\approx 11$ days earlier than previously reported in the literature for this object. Interestingly around two months past maximum, the NIR spectrum of SN~2016adj begins to exhibit H features, with a +97~d medium resolution spectrum revealing both Paschen and Bracket lines with absorption minima of $\sim 2000$ km/s, full-width-half-maximum emission velocities of $\sim 1000$ km/s, and emission line ratios consistent with a dense emission region. We speculate these attributes are due to circumstellar interaction (CSI) between the rapidly expanding SN ejecta and a H-rich shell of material formed during the pre-SN phase. A bolometric light curve is constructed and a semi-analytical model fit suggests the supernova synthesized 0.5 solar masses of $^{56}$Ni and ejected 4.2 solar masses of material, though these values should be approached with caution given the large uncertainties associated with the adopted reddening parameters, possible CSI contamination, and known light echo emission. Finally, inspection of Hubble Space Telescope archival data yielded no progenitor detection., Comment: Submitted to A&A, comments are welcome

Over-parameterized models like deep nets and random forests have become very popular in machine learning. However, the natural goals of continuity and differentiability, common in regression models, are now often ignored in modern overparametrized, locally-adaptive models. We propose a general framework to construct a global continuous and differentiable model based on a weighted average of locally learned models in corresponding local regions. This model is competitive in dealing with data with different densities or scales of function values in different local regions. We demonstrate that when we mix kernel ridge and polynomial regression terms in the local models, and stitch them together continuously, we achieve faster statistical convergence in theory and improved performance in various practical settings.

We present an analysis of Type Ia Supernovae (SNe~Ia) from both the Carnegie Supernova Project~I (CSP-I) and II (CSP-II), and extend the Hubble diagram from the optical to the near-infrared wavelengths ($uBgVriYJH$). We calculate the Hubble constant, $H_0$, using various distance calibrators: Cepheids, Tip of the Red Giant Branch (TRGB), and Surface Brightness Fluctuations (SBF). Combining all methods of calibrations, we derive $\rm H_0=71.76 \pm 0.58 \ (stat) \pm 1.19 \ (sys) \ km \ s^{-1} \ Mpc^{-1}$ from $B$-band, and $\rm H_0=73.22 \pm 0.68 \ (stat) \pm 1.28 \ (sys) \ km \ s^{-1} \ Mpc^{-1}$ from $H$-band. By assigning equal weight to the Cepheid, TRGB, and SBF calibrators, we derive the systematic errors required for consistency in the first rung of the distance ladder, resulting in a systematic error of $1.2\sim 1.3 \rm \ km \ s^{-1} \ Mpc^{-1}$ in $H_0$. As a result, relative to the statistics-only uncertainty, the tension between the late-time $H_0$ we derive by combining the various distance calibrators and the early-time $H_0$ from the Cosmic Microwave Background is reduced. The highest precision in SN~Ia luminosity is found in the $Y$ band ($0.12\pm0.01$ mag), as defined by the intrinsic scatter ($\sigma_{int}$). We revisit SN~Ia Hubble residual-host mass correlations and recover previous results that these correlations do not change significantly between the optical and the near-infrared wavelengths. Finally, SNe~Ia that explode beyond 10 kpc from their host centers exhibit smaller dispersion in their luminosity, confirming our earlier findings. Reduced effect of dust in the outskirt of hosts may be responsible for this effect., Comment: Revised calculations are made. Will be resubmitted to ApJ

We introduce the notion of an $\varepsilon$-cover for a kernel range space. A kernel range space concerns a set of points $X \subset \mathbb{R}^d$ and the space of all queries by a fixed kernel (e.g., a Gaussian kernel $K(p,\cdot) = \exp(-\|p-\cdot\|^2)$). For a point set $X$ of size $n$, a query returns a vector of values $R_p \in \mathbb{R}^n$, where the $i$th coordinate $(R_p)_i = K(p,x_i)$ for $x_i \in X$. An $\varepsilon$-cover is a subset of points $Q \subset \mathbb{R}^d$ so for any $p \in \mathbb{R}^d$ that $\frac{1}{n} \|R_p - R_q\|_1\leq \varepsilon$ for some $q \in Q$. This is a smooth analog of Haussler's notion of $\varepsilon$-covers for combinatorial range spaces (e.g., defined by subsets of points within a ball query) where the resulting vectors $R_p$ are in $\{0,1\}^n$ instead of $[0,1]^n$. The kernel versions of these range spaces show up in data analysis tasks where the coordinates may be uncertain or imprecise, and hence one wishes to add some flexibility in the notion of inside and outside of a query range. Our main result is that, unlike combinatorial range spaces, the size of kernel $\varepsilon$-covers is independent of the input size $n$ and dimension $d$. We obtain a bound of $(1/\varepsilon)^{\tilde O(1/\varepsilon^2)}$, where $\tilde{O}(f(1/\varepsilon))$ hides log factors in $(1/\varepsilon)$ that can depend on the kernel. This implies that by relaxing the notion of boundaries in range queries, eventually the curse of dimensionality disappears, and may help explain the success of machine learning in very high-dimensions. We also complement this result with a lower bound of almost $(1/\varepsilon)^{\Omega(1/\varepsilon)}$, showing the exponential dependence on $1/\varepsilon$ is necessary., Comment: 27 pages

In linear distance metric learning, we are given data in one Euclidean metric space and the goal is to find an appropriate linear map to another Euclidean metric space which respects certain distance conditions as much as possible. In this paper, we formalize a simple and elegant method which reduces to a general continuous convex loss optimization problem, and for different noise models we derive the corresponding loss functions. We show that even if the data is noisy, the ground truth linear metric can be learned with any precision provided access to enough samples, and we provide a corresponding sample complexity bound. Moreover, we present an effective way to truncate the learned model to a low-rank model that can provably maintain the accuracy in loss function and in parameters -- the first such results of this type. Several experimental observations on synthetic and real data sets support and inform our theoretical results., Comment: 52 pages

Bayesian Decision Trees (DTs) are generally considered a more advanced and accurate model than a regular Decision Tree (DT) because they can handle complex and uncertain data. Existing work on Bayesian DTs uses Markov Chain Monte Carlo (MCMC) with an accept-reject mechanism and sample using naive proposals to proceed to the next iteration, which can be slow because of the burn-in time needed. We can reduce the burn-in period by proposing a more sophisticated way of sampling or by designing a different numerical Bayesian approach. In this paper, we propose a replacement of the MCMC with an inherently parallel algorithm, the Sequential Monte Carlo (SMC), and a more effective sampling strategy inspired by the Evolutionary Algorithms (EA). Experiments show that SMC combined with the EA can produce more accurate results compared to MCMC in 100 times fewer iterations., Comment: arXiv admin note: text overlap with arXiv:2301.09090

Ranking is at the core of many artificial intelligence (AI) applications, including search engines, recommender systems, etc. Modern ranking systems are often constructed with learning-to-rank (LTR) models built from user behavior signals. While previous studies have demonstrated the effectiveness of using user behavior signals (e.g., clicks) as both features and labels of LTR algorithms, we argue that existing LTR algorithms that indiscriminately treat behavior and non-behavior signals in input features could lead to suboptimal performance in practice. Particularly because user behavior signals often have strong correlations with the ranking objective and can only be collected on items that have already been shown to users, directly using behavior signals in LTR could create an exploitation bias that hurts the system performance in the long run. To address the exploitation bias, we propose EBRank, an empirical Bayes-based uncertainty-aware ranking algorithm. Specifically, to overcome exploitation bias brought by behavior features in ranking models, EBRank uses a sole non-behavior feature based prior model to get a prior estimation of relevance. In the dynamic training and serving of ranking systems, EBRank uses the observed user behaviors to update posterior relevance estimation instead of concatenating behaviors as features in ranking models. Besides, EBRank additionally applies an uncertainty-aware exploration strategy to explore actively, collect user behaviors for empirical Bayesian modeling and improve ranking performance. Experiments on three public datasets show that EBRank is effective, practical and significantly outperforms state-of-the-art ranking algorithms.

We present photometric and spectroscopic observations and analysis of SN 2021bxu (ATLAS21dov), a low-luminosity, fast-evolving Type IIb supernova (SN). SN 2021bxu is unique, showing a large initial decline in brightness followed by a short plateau phase. With $M_r = -15.93 \pm 0.16\, \mathrm{mag}$ during the plateau, it is at the lower end of the luminosity distribution of stripped-envelope supernovae (SE-SNe) and shows a distinct $\sim$10 day plateau not caused by H- or He-recombination. SN 2021bxu shows line velocities which are at least $\sim1500\,\mathrm{km\,s^{-1}}$ slower than typical SE-SNe. It is photometrically and spectroscopically similar to Type IIb SNe during the photospheric phases of evolution, with similarities to Ca-rich IIb SNe. We find that the bolometric light curve is best described by a composite model of shock interaction between the ejecta and an envelope of extended material, combined with a typical SN IIb powered by the radioactive decay of $^{56}$Ni. The best-fit parameters for SN 2021bxu include a $^{56}$Ni mass of $M_{\mathrm{Ni}} = 0.029^{+0.004}_{-0.005}\,\mathrm{M_{\odot}}$, an ejecta mass of $M_{\mathrm{ej}} = 0.61^{+0.06}_{-0.05}\,\mathrm{M_{\odot}}$, and an ejecta kinetic energy of $K_{\mathrm{ej}} = 8.8^{+1.1}_{-1.0} \times 10^{49}\, \mathrm{erg}$. From the fits to the properties of the extended material of Ca-rich IIb SNe we find a trend of decreasing envelope radius with increasing envelope mass. SN 2021bxu has $M_{\mathrm{Ni}}$ on the low end compared to SE-SNe and Ca-rich SNe in the literature, demonstrating that SN 2021bxu-like events are rare explosions in extreme areas of parameter space. The progenitor of SN 2021bxu is likely a low mass He star with an extended envelope., Comment: 18 pages, 15 figures, accepted to MNRAS