Evidential clustering is an approach to clustering in which cluster-membership uncertainty is represented by a collection of Dempster-Shafer mass functions forming an evidential partition. In this paper, we propose to construct these mass functions by bootstrapping finite mixture models. In the first step, we compute b…
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48 results for “probability mass functions”
A new method calculates fractional moments using the moment-generating function.
problem Computing fractional moments from probability densities.
method Integral framework based on moment-generating function.
result Exact integral expressions for various types of moments.
Proposes a method to reconcile count time series forecasts.
problem No formal framework for probabilistic reconciliation of count time series.
method Generalizes Bayes' rule for reconciling real-valued and count variables.
result Improves forecast accuracy for count variables compared to Gaussian reconciliation.
We revisit logistic regression and its nonlinear extensions, including multilayer feedforward neural networks, by showing that these classifiers can be viewed as converting input or higher-level features into Dempster-Shafer mass functions and aggregating them by Dempster's rule of combination. The probabilistic output…
Identifies conditions for multiple invariant probabilities in Markov kernels.
problem Global irreducibility and recurrence do not guarantee uniqueness of invariant probabilities.
method Uses Jordan decomposition of the difference of two invariant probabilities.
result A Markov kernel has more than one invariant probability if and only if it admits a visible absorbing decomposition.
Local mappings relate dual and primal factor graphs for efficient marginal probability estimation.
problem Efficient estimation of marginal probabilities in statistical physics models.
method Local mappings based on Fourier transform of local factors, applied to Ising, Potts, and clock models.
result Local extrema of fixed points are at phase transition points, and the mapping facilitates efficient estimation.
Quantified limits of nuclear stability beyond drip lines.
problem Predicting nuclear stability beyond known isotopes.
method Microscopic nuclear mass models, Bayesian methodology, Gaussian processes.
result Quantified predictions of one- and two-nucleon separation energies.
Novel concentration inequalities are obtained for the missing mass, i.e. the total probability mass of the outcomes not observed in the sample. We derive distribution-free deviation bounds with sublinear exponents in deviation size for missing mass and improve the results of Berend and Kontorovich (2013) and Yari Saeed…
The study uses statistical methods to analyze nuclear mass models.
problem Understanding the information content of nuclear masses from models.
method Bayesian calibration, Bayesian model averaging, chi-square correlation analysis, principal component analysis.
result A dramatic parameter reduction can be achieved in both 4-parameter and 14-parameter models.
New method calibrates classifier probabilities with guaranteed coverage.
problem Inaccurate probability estimates by classifiers in high-risk applications.
method Adaptive temperature scaling algorithm for conformal prediction.
result Improves calibration error measures and standard metrics across various tasks.
This review explores entropy applications in data analysis and machine learning.
problem Characterizing probability mass distributions in data analysis and machine learning.
method Review of various entropy types and their applications.
result Entropy's versatility in data analysis and machine learning.
This paper shows that one cannot learn the probability of rare events without imposing further structural assumptions. The event of interest is that of obtaining an outcome outside the coverage of an i.i.d. sample from a discrete distribution. The probability of this event is referred to as the "missing mass". The impo…
Solves probabilistic Lambert problem connecting astrodynamics with optimal mass transport.
problem Determining spacecraft velocity for given positions with probabilistic constraints.
method Generalized optimal mass transport (OMT) and Schrödinger bridge (SBP) connections.
result Existence and uniqueness of solution for probabilistic Lambert problem.
Given samples from a population of individuals belonging to different types with unknown proportions, how do we estimate the probability of discovering a new type at the -th draw? This is a classical problem in statistics, commonly referred to as the missing mass estimation problem. Recent results by Ohannes…
A definition of the mass aspect function for weakly regular asymptotically hyperbolic manifoldsmath.DG
Unified definition of mass aspect function for weakly regular hyperbolic manifolds.
problem Ambiguity in mass definition for asymptotically hyperbolic manifolds.
method Introduced an ADM-style mass aspect function for broad asymptotics and low regularity.
result Unified mass aspect function exhibits favorable covariance properties.
Study on residual Monge-Ampère mass for symmetric plurisubharmonic functions.
problem Estimating the residual Monge-Ampère mass of symmetric plurisubharmonic functions with isolated singularities.
method Utilized Sasakian geometry to derive estimates on the residual mass in relation to Lelong numbers.
result Partially resolved the zero mass conjecture by Guedj and Rashkovskii.
New method for summarizing ranking distributions using consensus ranking distributions.
problem Summarizing ranking distributions efficiently and accurately.
method Introducing consensus ranking distributions and a top-down tree-structured statistical algorithm.
result Optimal distortion can be expressed as a function of pairwise probabilities, enabling efficient learning methods.
Study on residual Monge-Ampère mass for symmetric plurisubharmonic functions.
problem Analyzing the residual Monge-Ampère mass of symmetric plurisubharmonic functions.
method Proved zero mass for functions with zero Lelong number at origin and -invariance.
result Zero mass conjecture answered for symmetric functions.
In this article, we classify the set of asymptotic mass-like invariants for asymptotically hyperbolic metrics. It turns out that the standard mass is just one example (but probably the most important one) among the two families of invariants we find. These invariants are attached to finite-dimensional representations o…
The paper connects mass, harmonic functions, and capacity in asymptotically flat 3-manifolds.
problem Connections among ADM mass, harmonic functions, and capacity in asymptotically flat 3-manifolds.
method New formulae for ADM mass via harmonic functions, monotone quantities, and geometric inequalities.
result The mass-to-capacity ratio is bounded below by 1 - sqrt(normalized Willmore functional of the boundary).
A novel notion of barycenter for probability distributions based on optimal weak mass transportstat.ML
A new method for averaging probability distributions based on optimal weak mass transport.
problem Averaging probability distributions in a geometric way.
method Weak barycenters based on optimal weak mass transport.
result Extracts common geometric information shared by all input distributions.
Expected centre of mass for random embeddings is constant.
problem Understanding the expected centre of mass for random embeddings.
method Analyzing the Haar measure and Gaussian unitary ensemble on SL(N, C).
result The expectation of the centre of mass is a constant multiple of the identity matrix.
Global existence and geometry of constant mass aspect function foliation in perturbed Schwarzschild spacetime studied.
problem Null Penrose inequality on a null hypersurface.
method Global existence of constant mass aspect function foliation on a nearly spherically symmetric incoming null hypersurface in a vacuum perturbed Schwarzschild spacetime.
result Geometry of the constant mass aspect function foliation compared to the spherically symmetric foliation in the Schwarzschild spacetime.
The paper defines a new mass quantity for 3-manifolds and proves a positive mass theorem.
problem Proving the positive mass theorem for a new geometric quantity.
method Defining -ADM mass and using a monotonicity formula.
result Established a relative positive mass theorem for asymptotically flat 3-manifolds.
We propose a correlated stochastic process of which the novel non-Gaussian probability mass function is constructed by exactly solving moment generating function. The calculation of cumulants and auto-correlation shows that the process is convergent and scale invariant in the large but finite number limit. We demonstra…
Proves Green function rigidity for specific operators and obtains new ADM mass formula.
problem Proving Green function rigidity for specific operators and obtaining new ADM mass formula.
method Positive mass theorem and positive energy theorem for Paneitz operator.
result Obtained new formula for the ADM mass of asymptotically flat hypersurfaces.
Study calculates mass of special polyhedra in hyperbolic space.
problem Evaluating mass in hyperbolic geometry.
method Used upper half space model and special polyhedra.
result Evaluated mass functional on polyhedra.
Study on residual Monge-Ampère mass of complex functions with directional Lipschitz continuity.
problem Estimating the residual Monge-Ampère mass of plurisubharmonic functions.
method General decomposition formula under Sasakian structure, -apriori estimate, upper-bound estimate on residual mass.
result Upper-bound estimate on residual mass for uniformly directional Lipschitz continuity confirmed.
New positive mass theorem for hyperbolic 3-manifolds using Green functions.
problem Proving a positive mass theorem for asymptotically hyperbolic 3-manifolds.
method Using a monotonicity formula for the Green function of the Laplace operator.
result Established a new positive mass theorem for three-dimensional manifolds.
Unified framework for analyzing gradient flows of measures with exponential decay of entropy.
problem Analyzing exponential decay of entropy functionals in gradient flows of measures.
method Characterization of global exponential decay behaviors using Hellinger-Kantorovich geometry, shape-mass decomposition, and Polyak-Łojasiewicz-type inequalities.
result Unified theoretical framework for gradient flows with complete analysis of exponential decay behaviors.
We are concerned with obtaining novel concentration inequalities for the missing mass, i.e. the total probability mass of the outcomes not observed in the sample. We not only derive - for the first time - distribution-free Bernstein-like deviation bounds with sublinear exponents in deviation size for missing mass, but …
New formulae identify discrete probability laws without needing normalization constants.
problem Characterizing non-normalized discrete probability distributions.
method Derive explicit formulae for mass functions using Stein's method.
result Developed tools for solving statistical problems without normalization constants.
We derive a positive mass theorem for asymptotically flat manifolds with boundary whose mean curvature satisfies a sharp estimate involving the conformal Green's function. The theorem also holds if the conformal Green's function is replaced by the standard Green's function for the Laplacian operator. As an application,…
A Quasi-Local Massmath.DG
Defines a new quasi-local mass related to spacetime harmonic functions.
problem Calculating mass for regions in spacetime.
method Quasi-local proof using spacetime harmonic functions and embeddings into Minkowski space.
result Establishes positivity and vanishing conditions for the new quasi-local mass.
A mass-type invariant for smooth metric measure spaces and its relation with the fractional Yamabe problem
problem Defining and analyzing a mass-type invariant for smooth metric measure spaces
method Defining a mass-type quantity and showing its geometric invariance properties
result The mass-type quantity has a close relation with the fractional Yamabe problem and the relevant Green's function
Proposes a new framework for uncertainty evaluation in ML classification models.
problem Uncertainty evaluation for ML classification models not addressed by existing metrological guidelines.
method Develops a metrological framework based on probability mass functions and summary statistics.
result Extends the GUM to uncertainty for nominal properties, applicable to ML classification models.
New methods using spacetime harmonic functions solve geometric inequalities.
problem Geometric inequalities involving mass in spacetime.
method Utilizing spacetime harmonic functions and other elliptic equations.
result Novel concept of total mass and proof of positive mass theorem.
New algorithm detects anomalies by forcing samples to displace mass in low-density regions.
problem Detecting anomalies in datasets.
method Mass Repulsing Optimal Transport (MROT) approach.
result Our algorithm improves anomaly detection over existing methods.
Derives monotonic quantities for -harmonic functions on manifolds.
problem Understanding -harmonic functions on manifolds with nonnegative scalar curvature.
method Derives local and global monotonic quantities associated with -harmonic functions.
result Establishes inequalities relating mass, capacity, and Willmore functional.
The Riemannian center of mass was constructed in [GrKa] (1973). In [GKR1, GKR2, Gr, Ka, BuKa] (1974-1981) it was successfully applied with more refined estimates. Probably in 1990 someone renamed it without justification into karcher mean and references to the older papers were omitted by those using the new name. As a…
SDE automatically recovers interpretable discrete distributions.
problem Limited interpretable discrete probability laws.
method Unsupervised framework using symbolic density estimation.
result Accurately recovers interpretable discrete distributions.
We define a generalized mass for asymptotically flat manifolds using some higher order symmetric function of the curvature tensor. This mass is non-negative when the manifold is locally conformally flat and the curvature vanishes at infinity. In addition, with the above assumptions, if the mass is zero, then, nea…
The mass, or binding energy, is the basis property of the atomic nucleus. It determines its stability, and reaction and decay rates. Quantifying the nuclear binding is important for understanding the origin of elements in the universe. The astrophysical processes responsible for the nucleosynthesis in stars often take …
GT estimator shows convergence for Markov samples, improving i.i.d. results.
problem Estimating missing mass in Markov samples.
method Analyzed convergence of Good-Turing estimator for Markov samples, considering spectral properties of transition matrices.
result The convergence of the GT estimator for Markov samples depends on the spectral properties of the transition matrices, leading to a new minimax rate of for rank-2 Markov chains.
We propose a deep-learning approach based on generative adversarial networks (GANs) to reduce noise in weak lensing mass maps under realistic conditions. We apply image-to-image translation using conditional GANs to the mass map obtained from the first-year data of Subaru Hyper Suprime-Cam (HSC) survey. We train the co…
The paper proves a discrete positive mass theorem for graphs.
problem Formulating and proving a discrete positive mass theorem for graphs.
method Introducing asymptotically flat graphs, defining ADM mass, and using discrete harmonic functions.
result An asymptotically flat graph with non-negative Ricci curvature is isomorphic to the standard grid graph.
The paper calculates mass and volume of Einstein metrics in four dimensions.
problem Calculating mass and volume of Einstein metrics in four dimensions.
method Using Green's function and conformal laplacian, the paper expresses ADM mass as an integral and proves a mass-volume inequality.
result Proves a lower bound for the mass of a metric in terms of its volume, and various mass gap theorems.
CNFs learn on manifolds using PPD, improving likelihood and sample quality.
problem Training CNFs on manifolds efficiently and accurately.
method Minimizing PPD, a novel divergence, to train CNFs on manifolds.
result CNFs trained with PPD achieve state-of-the-art results on manifold benchmarks.