This paper presents the key algorithmic techniques behind CatBoost, a new gradient boosting toolkit. Their combination leads to CatBoost outperforming other publicly available boosting implementations in terms of quality on a variety of datasets. Two critical algorithmic advances introduced in CatBoost are the implementation of ordered boosting, a permutation-driven alternative to the classic algorithm, and an innovative algorithm for processing categorical features. Both techniques were created to fight a prediction shift caused by a special kind of target leakage present in all currently existing implementations of gradient boosting algorithms. In this paper, we provide a detailed analysis of this problem and demonstrate that proposed algorithms solve it effectively, leading to excellent empirical results.

3D scanning pose change output reconstruction textured reconstruction large variety of examples 3D print Figure 1: With our system, users can scan themselves with a single 3D sensor by rotating the same pose for a few different views (typically eight, ⇠45 degrees apart) to cover the full body. Our method robustly registers and merges different scans into a watertight surface with consistent texture in spite of shape changes during repositioning, and lighting differences between the scans. These surfaces are suitable for applications such as online avatars or 3D printing (the miniature shown here was printed using a ZPrinter 650.) AbstractWe develop an automatic pipeline that allows ordinary users to capture complete and fully textured 3D models of themselves in minutes, using only a single Kinect sensor, in the uncontrolled lighting environment of their own home. Our method requires neither a turntable nor a second operator, and is robust to the small deformations and changes of pose that inevitably arise during scanning. After the users rotate themselves with the same pose for a few scans from different views, our system stitches together the captured scans using multi-view non-rigid registration, and produces watertight final models. To ensure consistent texturing, we recover the underlying albedo from each scanned texture and generate seamless global textures using Poisson blending. Despite the minimal requirements we place on the hardware and users, our method is suitable for full body capture of challenging scenes that cannot be handled well using previous methods, such as those involving loose clothing, complex poses, and props.

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3D data is a valuable asset the computer vision filed as it provides rich information about the full geometry of sensed objects and scenes. Recently, with the availability of both large 3D datasets and computational power, it is today possible to consider applying deep learning to learn specific tasks on 3D data such as segmentation, recognition and correspondence. Depending on the considered 3D data representation, different challenges may be foreseen in using existent deep learning architectures. In this work, we provide a comprehensive overview about various 3D data representations highlighting the difference between Euclidean and non-Euclidean ones. We also discuss how Deep Learning methods are applied on each representation, analyzing the challenges to overcome.Concepts: • General and references → Surveys and overviews; • Computing methodologies → 3D Deep Learning; 3D computer vision applications; 3D data representations;

We generalize the Abel-Ruffini theorem to arbitrary dimension, i.e. classify general square systems of polynomial equations solvable by radicals. In most cases, they reduce to systems whose tuples of Newton polytopes have mixed volume not exceeding 4. The proof is based on topological Galois theory, which ensures non-solvability by any formula involving quadratures and single-valued functions, and the computation of the monodromy group of a general system of equations, which may be of independent interest.

We classify generic systems of polynomial equations with a single solution, or, equivalently, collections of lattice polytopes of minimal positive mixed volume. As a byproduct, this classification provides an algorithm to evaluate the single solution of such a system. See Section 2 for the proof. Here and in what follows, the volume forms in the subspace U ⊂ V and in the quotient space V /U are induced by the lattices U = U ∩ V and V/U respectively. Condition (1) implies that the k polytopes in (2) generate the whole simplex.Example. Any pair of lattice polygons of mixed area 1 is equal (up to translations and an authomorphism of Z 2 ) to exactly one of the following pairs (with a b 0):The question of classifying lattice polytopes of small mixed volume is particularly motivated by the study of codimensions of discriminants (see, e.g., [5, Theorem 3.13], or [2] for details). Theorem 1 was conjectured in [5, Conjecture 3.16], and its special case of full-dimensional polytopes was proved in [2, Proposition 2.7].The mixed volume is related to algebra by the Kouchnirenko-Bernstein formula: a system of n polynomial equations of n variables with Newton polytopes N 1 , N 2 . . . , N n and generic coefficients has MV(N 1 , N 2 , . . . , N n ) solutions in the complex torus (C \ 0) n , see [1]. Thus, Theorem 1 classifies all generic systems of polynomial equations with a unique solution. By a general Gröbner basis or Galois theory argument, the solution of such a system admits a rational expression in terms of the coefficients of the system, and Theorem 1 provides an explicit construction for it (by induction on n): I) upon a certain monomial change of variables, k of the n equations become linear (nonhomogeneous) equations of k variables, from which the k variables can be evaluated; II) after the substitution of the evaluated variables in the other equations, we obtain n − k generic equations of n − k variables with a unique solution and proceed to the next group of simultaneously linearizable equations.Example. In order to solve a system a + bxy = 0, f (xy) + yg(xy) = 0, we first make a monomial change xy = u, y = v, then solve the first equation a + bu = 0, linear in u, and obtain u = −a/b, then put the result to the second equation f (−a/b) + vg(−a/b) = 0, linear in v, and obtain v = −f (−a/b)/g(−a/b). Theorem 1 ensures that such an obvious approach works in any dimension for square systems with a single solution. This algorithm addresses the simplest possible problem in the field of efficient solving of polynomial systems with few monomials/solutions (see, e.g., [3] and [8] for motivation and recent advances in some other related problems). A polynomial-time implementation of this scheme is described in Section 6. An example of further classification (square systems of ≤3 equations with two solutions) is given in Section 7.

This work proposes a novel 3D Deformation Signature (3DS) to represent a 3D deformation signal for 3D Dynamic Face Recognition. 3DS is computed given a non-linear 6D-space representation which guarantees physically plausible 3D deformations. A unique deformation indicator is computed per triangle in a triangulated mesh as a ratio derived from scale and in-plane deformation in the canonical space. These indicators, concatenated, construct the 3DS for each temporal instance. There is a pressing need of non-intrusive bio-metric measurements in domains like surveillance and security. By construction, 3DS is a non-intrusive facial measurement that is resistant to common security attacks like presentation, template and adversarial attacks. Two dynamic datasets (BU4DFE and COMA) were examined, in a standard classification framework, to evaluate 3DS. A first rank recognition accuracy of 99.9%, that outperforms existing literature, was achieved. Assuming an open-world setting, 99.97% accuracy was attained in detecting unseen distractors.

Given a repeatedly issued query and a document with a notyet-confirmed potential to satisfy the users' needs, a search system should place this document on a high position in order to gather user feedback and obtain a more confident estimate of the document utility. On the other hand, the main objective of the search system is to maximize expected user satisfaction over a rather long period, what requires showing more relevant documents on average. The state-of-the-art approaches to solving this exploration-exploitation dilemma rely on strongly simplified settings making these approaches infeasible in practice. We improve the most flexible and pragmatic of them to handle some actual practical issues. The first one is utilizing prior information about queries and documents, the second is combining bandit-based learning approaches with a default production ranking algorithm. We show experimentally that our framework enables to significantly improve the ranking of a leading commercial search engine.