Paper addresses CPA line forecasting in online advertising mid-flight.
problem Forecasting ad campaign performance mid-flight considering bidding mechanisms.
method Generates relationships between metrics and optimization signals, estimates sensitivity, and characterizes advertiser spends vs. eCPA.
result Demonstrates promising accuracy in forecasting against actual deliveries.
New ROC tools assess predictive abilities for any linearly ordered outcomes.
problem Fundamental restriction in ROC analysis for non-dichotomous outcomes.
method ROC movies and UROC curves for linearly ordered outcomes.
result CPA equals AUC for binary outcomes and relates to Spearman's coefficient for pairwise distinct outcomes.
We analyzed the performance of a biologically inspired algorithm called the Corrected Projections Algorithm (CPA) when a sparseness constraint is required to unambiguously reconstruct an observed signal using atoms from an overcomplete dictionary. By changing the geometry of the estimation problem, CPA gives an analyti…
Chronic Pulmonary Aspergillosis (CPA) is a complex lung disease caused by infection with Aspergillus. Computed tomography (CT) images are frequently requested in patients with suspected and established disease, but the radiological signs on CT are difficult to quantify making accurate follow-up challenging. We propose …
CPAS uses machine learning to plan hospital resources for COVID-19.
problem Forecasting hospital resource demands during the COVID-19 pandemic.
method Combining machine learning algorithms with diverse data sources.
result CPAS successfully managed hospital resource planning in the UK.
Neural networks can represent complex piecewise functions efficiently.
problem Representing continuous piecewise affine functions with neural networks.
method Two hidden layers with ReLU activation, O(p) neurons for p pieces. result CPA functions can be represented by a neural network with linear size.
CPA framework assesses conditional validity of conformal prediction.
problem Challenges in evaluating conditional validity of conformal prediction.
method Reframes conditional coverage evaluation as a supervised learning task.
result Establishes convergence rates and proves CVI consistency.
Graph Neural Networks (GNNs) are powerful to learn the representation of graph-structured data. Most of the GNNs use the message-passing scheme, where the embedding of a node is iteratively updated by aggregating the information of its neighbors. To achieve a better expressive capability of node influences, attention m…
Conversion prediction plays an important role in online advertising since Cost-Per-Action (CPA) has become one of the primary campaign performance objectives in the industry. Unlike click prediction, conversions have different types in nature, and each type may be associated with different decisive factors. In this pap…
New EM algorithm improves deep generative network training.
problem Training deep generative networks with complex posterior and likelihood distributions.
method Derive analytical posterior and marginal distributions using CPA property, derive analytical EM algorithm.
result EM training yields higher likelihood than Variational Autoencoders (VAEs).
BN refines local partition geometry in piecewise-affine networks during training.
problem Understanding the effect of BN on the function realized during training in piecewise-affine networks.
method Analyzing the geometry of switching hyperplanes and affine-region partition conditioned on a mini-batch.
result BN increases expected local partition refinement in ReLU and piecewise-affine networks.
Deep network optimizes ad bidding for first-price auctions.
problem Optimizing bid prices for first-price auctions in online advertising.
method Introduced a deep distribution network for optimal bidding.
result Algorithm outperforms previous methods in terms of surplus and eCPX metrics.
Batch normalization improves deep networks by aligning their decision boundaries with data.
problem Improving the performance and generalization of deep networks.
method Theoretical analysis of batch normalization as a function approximation technique for continuous piecewise affine splines.
result Batch normalization adapts the geometry of a deep network's partition to match the data, improving learning and generalization.
The paper describes the geometric properties of line congruences' singularities.
problem Understanding the singularities of generic line congruences.
method Use of an equiaffine pair to define generic line congruences.
result Geometric description of folds, cusps, and swallowtails as singularities of generic line congruences.
This paper generalizes the envelope of mid-lines to intermediate lines for a plane curve.
problem Understanding the envelope of intermediate lines for a plane curve.
method Using singularity theory techniques to analyze the local behavior of the envelope of intermediate lines.
result The envelope of intermediate lines (EIL) is formed by three disconnected sets: AEIL, the curve itself, and IPTL. Study restricts line arrangements with odd points using topological arguments.
problem Restrictions on line arrangements with singular points of odd multiplicity.
method Topological arguments on locally-flat spheres in 4-manifolds.
result No line arrangement with 13 lines and only triple points exists.
A special group of transformations of the real line cannot act effectively on it.
problem Understanding the limitations of transformations on the real line.
method Analyzing the group of orientation-preserving quasi-isometries of the real line.
result The group of quasi-isometries of the real line cannot act effectively on the line.
Study Blaschke's asymptotic lines on surfaces in 3D space.
problem Characterize Blaschke's asymptotic lines on surfaces in 3D.
method Analyze binary differential equations near cusp and umbilic points.
result Describe Blaschke's asymptotic lines near Euclidean parabolic set.
Co-PLNet combines point and line predictions to improve wireframe parsing accuracy and efficiency.
problem Separate line and point predictions lead to inconsistent wireframes.
method Co-PLNet uses a Point-Line Prompt Encoder to convert early point detections into spatial prompts, which guide line refinement.
result Co-PLNet achieves better accuracy and robustness in wireframe parsing compared to existing methods.
Characterizes winding of braided vector fields in tubular domains.
problem Understanding the topology of braided vector fields in complex domains.
method Defines field line winding as a measure of entanglement, proving its uniqueness in classifying vector field topology.
result Field line winding uniquely classifies the topology of braided vector fields.
Classifies metric lines in Engel-type groups, a step towards solving sub-Riemannian manifold problems.
problem Classifying metric lines in Engel-type groups.
method Sequence method to study metric lines in jet space.
result Classified metric lines of Engel-type groups $\Eng(n)$.
New Calabi-Yau metrics with conical singularities are created near complex lines.
problem Creating Calabi-Yau metrics with conical singularities near complex lines.
method Using branched covering arguments to construct metrics with conical singularities.
result Calabi-Yau metrics with unstable conical singularities are successfully created.
New ML-based detection improves PMH signal detection in load-modulated MIMO systems.
problem Detecting PMH signals without prior CSI is challenging and computationally expensive.
method Proposes HEM-ML and HEM-KD schemes using EM and KD-tree for efficient detection.
result Achieves comparable detection results to optimal ML detector with reduced complexity.
A line arrangement of 3n lines in CP2 satisfies Hirzebruch property if each line intersect others in n+1 points. Hirzebruch asked if all such arrangements are related to finite complex reflection groups. We give a positive answer to this question in the case when the line arrangement in CP2 is…
The paper examines asymptotic lines of plane fields in 3D space.
problem Qualitative properties of asymptotic lines in plane fields.
method Analysis of null directions and Gaussian curvature.
result Asymptotic lines coincide with classical ones in completely integrable fields.
The paper explores reflection principles for lightlike line segments on maximal surfaces.
problem Reflection property does not hold for lightlike line segments on maximal surfaces.
method Analyzes reflection properties for lightlike line segments connecting shrinking singularities.
result Shows a kind of reflection principle for lightlike line segments on maximal surfaces.
Circular nets with spherical parameter lines have geometric properties related to Darboux cyclides and terminating Laplace sequences.
problem Discretizing surfaces with spherical curvature lines.
method Lie-geometric discretisation in terms of principal contact element nets.
result Circular nets with two families of spherical parameter lines are related to Darboux cyclides.
The paper explores graphons of line graphs from sparse finite graphs.
problem Estimating graph limits from sparse finite graphs.
method Mapping finite graphs to their line graphs and analyzing graphs with the square-degree property.
result Graphons of line graphs can distinguish between sparse graphs like star graphs and superlinear preferential attachment graphs.
Estimates cohomology dimensions for Nakano q-semipositive line bundles.
problem Estimating cohomology dimensions for Nakano q-semipositive line bundles.
method Asymptotic estimates for high tensor powers of semipositive line bundles over q-convex manifolds and various complex manifolds.
result Optimal order estimates for cohomology dimensions.
New method describes entanglement of straight lines in 3D space.
problem Tackles the geometry and topology of configurations of straight lines.
method Introduces direction matrices and a discrete motion principle.
result Shows n-crosses as links of pairwise connected unknots.
Shows CM line bundles are ample on K-stable varieties.
problem Ensuring CM line bundles are ample on K-stable varieties.
method Analyzes CM line bundles on K-stable varieties and their families.
result CM line bundles are ample on K-stable varieties with maximal variation.
Study proves Hodge symmetry on Oeljeklaus-Toma manifolds with line bundles.
problem Hodge symmetry on complex manifolds with line bundles.
method Analyzes Dolbeault cohomology of Oeljeklaus-Toma manifolds with holomorphic line bundles.
result Proves Hodge symmetry and vanishing/non-vanishing of Dolbeault cohomology.
We define a pseudo-inverse for line graphs using linear integer programming.
problem Not all graphs have a corresponding root graph, making the line graph operation non-invertible.
method Propose a linear integer program to edit the smallest number of edges in the line graph to recover a root graph.
result The pseudo-inverse operation is well-behaved and works in practice as shown by empirical experiments.
The paper finds two types of metric lines in curve spaces.
problem Classifying metric lines in jet spaces of curves.
method Established the existence of two families of metric lines in the 2-jet space of plane curves.
result Found precise criteria for identifying metric lines in sub-Riemannian geodesics.
We explain the bundle structures of the {\it Determinant line bundle} and the {\it Quillen determinant line bundle} considered on the connected component of the space of Fredholm operators including the identity operator in an intrinsic way. Then we show that these two are isomorphic and that they are non-trivial line …
The authors study smooth lines on projective planes over the algebra C of complex numbers, the algebra C^1 of double numbers, and the algebra C^0 of dual numbers. In the space RP^5, to these smooth lines there correspond families of straight lines describing point three-dimensional tangentially degenerate submanifolds …
Geometric quantization extended to big line bundles.
problem Quantization of line bundles with large curvature.
method Proving asymptotic isometry and submultiplicative norms equivalence, showing Mabuchi geodesic rays.
result Bounded submultiplicative filtrations on big line bundles lead to Mabuchi geodesic rays.
There is a natural duality between line congruences in R3 and surfaces in R4 that sends principal lines into asymptotic lines. The same correspondence takes the discriminant curve of a line congruence into the parabolic curve of the dual surface. Moreover, it takes the ridge curves to the flat r…
Line graph transformation aids graph isomorphism tests by excluding challenging graph properties.
problem Limited theoretical understanding of line graph transformation's impact on GNN models.
method Examined CFI and strongly regular graphs, showing line graph transformation helps WL tests distinguish these graphs.
result Line graph transformation aids WL tests in distinguishing challenging graph properties.
New BDEs reveal singular surfaces from line congruences.
problem Understanding binary differential equations associated with line congruences.
method Applied pointwise to quadratic differential forms, studying quotients of quadratic forms and associated polar lines.
result Introduced a new singular surface in Euclidean 3-space.
We give quantitative and qualitative results on the family of surfaces in CP3 containing finitely many twistor lines. We start by analyzing the ideal sheaf of a finite set of disjoint lines E. We prove that its general element is a smooth surface containing E and no other line. Afterwards we prove that …
Study conic-line arrangements of degree 7, finding their topology and components.
problem Understanding the topology and components of conic-line arrangements of degree 7.
method Examined the embedded topology using SageMath and Sirocco package.
result Determined the number of connected components and fundamental groups.
We investigate several topological and combinatorial properties of line arrangements. We associate to a line arrangement a link obtained by intersecting the arrangement with some sphere. Several topics are discussed: (a) some link configurations can be realized by complex line arrangements but not by real line arrangem…
The paper classifies singularities of line congruences in 4D space.
problem Classifying singularities of line congruences in 4D space.
method Generic classification approach for 3-parameter line congruences and Blaschke normal congruences.
result Generic classification of singularities of 3-parameter line congruences in R4. Study three discrete envelope types of polygon bisection lines.
problem Understanding different envelope types of polygon bisection lines.
method Examined three distinct notions of discrete envelopes.
result Connected three different notions of discrete envelopes.
The Samuelson condition is not satisfied by tangent lines of quadratic curves.
problem Area condition for Lagrangian 2-web
method Show that the Samuelson condition is not satisfied
result The Samuelson condition is not satisfied by tangent lines of quadratic curves.
Study curvature lines of a vector field on surfaces.
problem Behavior of curvature lines at umbilical points.
method Analyzes transversal eqüiaffine vector fields on surfaces.
result Behavior of curvature lines at isolated umbilical points.
A cylindrical stretch line is a stretch line, in the sense of Thurston, whose horocyclic lamination is a weighted multicurve. In this paper, we show that two correctly parameterized cylindrical lines are parallel if and only if these lines converge towards the same point in Thurston's boundary of Teichmüller space.