This paper studies geometrical structure of the manifold of escort probability distributions and shows its new applicability to information science. In order to realize escort probabilities we use a conformal transformation that flattens so-called alpha-geometry of the space of discrete probability distributions, which…
NNLMs optimize poorly for word probabilities due to embedding space structure.
problem NNLMs assign suboptimal probabilities to some words.
method Analyzed the inductive bias of NNLMs and the structure of word embeddings.
result Words on the convex hull have bounded probability, affecting others.
Extends neural network approximation to probability measures and tree-structured data.
problem Universal approximation of functions on probability measures and tree-structured domains.
method Proof of neural network density in probability measure spaces and Cartesian products.
result Universal approximation theorem for tree-structured domains, including JSON.
Bayesian method for high-dimensional categorical data analysis.
problem Difficulties in probability modeling for high-dimensional data.
method Bayesian learning of clique tree structure.
result Optimal clique tree structure for probability modeling.
The study explores special submanifolds in the probability simplex with unique geometric properties.
problem Exploring special submanifolds in the probability simplex.
method Algebraic characterization and classification of doubly autoparallel submanifolds.
result Characterization and classification of doubly autoparallel submanifolds on the probability simplex.
We study the problem of learning Bayesian network structures from data. Koivisto and Sood (2004) and Koivisto (2006) presented algorithms that can compute the exact marginal posterior probability of a subnetwork, e.g., a single edge, in O(n2n) time and the posterior probabilities for all n(n-1) potential edges in O(n2n…
Risk measures are linked to probability structures, and a maximal domain is constructed.
problem Linking risk measures to probability structures and defining a maximal domain.
method Constructing a maximal domain respecting ambiguity and discussing properties.
result A meaningful underlying probability structure is implied by risk measures.
A Bayesian framework models dynamic probability predictions over time.
problem Dynamic probability predictions over time in various settings.
method Gaussian latent information martingale (GLIM) framework.
result GLIM outperforms baseline methods in predicting future uncertainties.
Novel unsupervised feature selection method using multi-step Markov transition probability.
problem Neglected relationships between non-adjacent data points in feature selection.
method MMFS (Multi-step Markov transition probability for Feature Selection) approach, employing positive and negative viewpoints.
result MMFS effectively maintains data structure in unsupervised feature selection.
A non-trivial probability structure is evident in the binary data extracted from the up/down price movements of very high frequency data such as tick-by-tick data for USD/JPY. In this paper, we analyze the Sony bank USD/JPY rates, ignoring the small deviations from the market price. We then show there is a similar non-…
The paper proposes a method to learn Bayesian networks with low rank conditional probability tables.
problem Learning the structure of Bayesian networks efficiently.
method Introduces low rankness for conditional probability tables, connects to Fourier transformation, and proposes a polynomial time algorithm.
result Correctly recovers the true directed structure of a low rank Bayesian network with few queries and polynomial samples.
New method for matrix completion under complex missing data patterns.
problem Matrix completion with complex missing data patterns.
method Estimate the probability matrix of observation via low-rank matrix estimation and use inverse probabilities weighting to complete the target matrix.
result Optimal asymptotic convergence rates for observation probabilities and target matrix estimation.
Paper examines trade/no trade patterns in illiquid stocks, highlighting effects of varying zero returns probabilities.
problem Detecting long-run trade/no trade effects in illiquid stocks with varying zero returns probabilities.
method Proposes a framework considering constant and time-varying zero returns probabilities, analyzing trade/no trade categorical sequences.
result Long-run trade/no trade effects may be spuriously detected in presence of non-constant zero returns probabilities.
Models predict probabilities of causation from limited data.
problem Estimating probabilities of causation requires unreliable or impractical experimental and observational data.
method Proposed Exact-MLP and Mask-MLP models trained on reliable subpopulations.
result Models achieve average MAEs of roughly 0.03, reducing MAE by 80%.
This research embeds data as discrete probability distributions in Wasserstein spaces, capturing semantic structures more effectively.
problem Limitations of Euclidean embeddings in capturing latent semantic structures.
method Learning embeddings into entropic Wasserstein spaces, capturing semantic information in Wasserstein distance.
result Wasserstein embeddings can embed a wider variety of metric structures with smaller distortion than Euclidean embeddings.
Paper axiomatizes interventional probability distributions.
problem Causal inference and intervention.
method Axiomatization of interventional families.
result Markovian property of intervened distributions.
The paper explores geometry of probability measures and barycenter maps.
problem Understanding the space of probability measures and their barycenter.
method Information geometry, Fisher metric, dualistic structures, divergences, geodesics.
result Recent developments in the geometry of probability measures and barycenter.
Paper constructs unfaithful probability distributions in binary causal graphs.
problem Unfaithful probability distributions in binary causal graphs.
method Constructs unfaithful probability distributions in binary causal graphs.
result Examples of unfaithful probability distributions in binary causal graphs.
Investigates probability of error in structured thresholding bandit problems.
problem Probability of misclassifying arms in structured thresholding bandit problems.
method Analyzes two shape constraints: monotonic increasing and concave sequences of arm means.
result Upper and lower bounds for the probability of error match up to constants in the problem dependent regime.
A new method for comparing measures in different spaces using flow alignment.
problem Comparing probability measures in different metric spaces with computational efficiency.
method Flow-based Alignment (\FlowAlign) and Depth-based Alignment (\DepthAlign) using tree structures.
result Flow-based Alignment and Depth-based Alignment are pseudo-distances and scalable for large-scale applications.
The paper analyzes regret in online recommendation systems with constraints.
problem Analyzing regret in online recommendation systems with user-item constraints.
method Theoretical analysis and algorithm design considering user-item constraints and unknown probabilities.
result Derives regret lower bounds and algorithms achieving these limits for various structural assumptions.
Unified framework models multiple financial and insurance term structures.
problem Modeling multiple term structures in various markets.
method Extended Heath-Jarrow-Morton (HJM) approach under real-world probability.
result Characterization of local martingale deflators and existence of affine realizations.
Researchers derive a formula for Brownian motion transition probability in a specific octant.
problem Computing default probabilities and credit valuation adjustments in structural credit models.
method Semi-analytic formula derived using separation of variables in spherical coordinates, followed by numerical methods to solve the resulting eigenvalue problem.
result A solution to the transition probability problem expressed as an expansion into special functions and an eigenvalue.
Active Kriging Monte Carlo simulation method with conformal certification for failure probability estimation
problem Failure probability estimation in structural reliability analysis
method Active learning framework with conformal prediction
result Improved uncertainty quantification and reliability of failure probability estimates
The paper improves the probability flow ODE sampler for faster sampling of natural images.
problem Improving the convergence rate of the probability flow ODE sampler.
method Adapting the probability flow ODE sampler to exploit intrinsic low-dimensional structures in natural image data.
result Achieves a dimension-free convergence rate of O(k/T) in total variation distance, improving upon existing results. Entropy data replaces classical charts for smooth manifolds.
problem Establishing smooth structures on topological manifolds.
method Using entropy data to define admissible coordinate functions and reconstruct smooth atlases.
result Entropy-smooth structures are equivalent to classical smooth structures and stable under perturbations.
Estimates growth of reciprocal classes in Hecke groups.
problem Estimating the growth of reciprocal conjugacy classes in Hecke groups.
method Using free product structure and word lengths of reciprocal elements, with tools from basic probability theory.
result Estimates the asymptotic growth of reciprocal conjugacy classes in Hecke groups.
Detects missing tensor signals in a KS subspace with high probability.
problem Detecting tensor signals with many missing entities in a KS subspace.
method Projecting the signal onto the KS subspace and bounding residual energy.
result Reliable detection is possible if the missing signal cardinality exceeds KS subspace dimensions.
GISST interprets GNNs by combining attention and sparsity for graph structure and node feature importance.
problem Lack of joint consideration of graph structure and node features in GNN interpretation.
method Model-agnostic framework using attention mechanism and sparsity regularization.
result GISST achieves superior node feature and edge explanation precision in synthetic and real-world datasets.
Novel algorithm speeds up computation of Sobolev IPM for graph-based probability measures.
problem Efficient computation of Sobolev IPM for graph-based probability measures.
method Established relation between Sobolev norm and weighted Lp-norm, proposed novel regularization, leveraged graph structure. result Proposed regularized Sobolev IPM provides closed-form expression for fast computation.
Gradient flows on distributions of distributions for machine learning tasks.
problem Designing gradient flows for datasets of probability distributions.
method Representing classes as conditional distributions, modeling datasets as mixture distributions, using Wasserstein over Wasserstein (WoW) distance and gradients.
result Demonstrated gradient flows for dataset transfer and distillation tasks.
The estimation of probabilities of network edges from the observed adjacency matrix has important applications to predicting missing links and network denoising. It has usually been addressed by estimating the graphon, a function that determines the matrix of edge probabilities, but this is ill-defined without strong a…
Quantum probability theory reveals hidden structure in joint probability distributions.
problem Understanding hidden structure in joint probability distributions.
method Modeling joint probability distributions as density operators and applying partial trace.
result Decoding extra information in reduced density operators that captures subsystem interactions.
SS-GEN simulates rare events in heavy and light-tailed data.
problem Estimating probabilities of extreme events in multivariate data.
method Self-Similar Generative Estimation (SS-GEN) decomposes tail distribution into radial and angular components.
result SS-GEN generates representative extreme scenarios and estimates rare-event probabilities beyond observed data.
Paper introduces Generalized Naive Bayes for better data fitting.
problem Improving Naive Bayes for better data fitting.
method Developed new greedy and optimal algorithms for GNB.
result Proves GNB fits data at least as well as classical NB.
Paper uses algebraic signatures to identify probabilistic structures in empirical data.
problem Identifying probabilistic structure from observed binomials in empirical probability tensors.
method Treating vanishing binomials as algebraic signatures, matching signatures to identify models without parameter estimation.
result The method successfully identified rank-one structures in real language data, revealing interpretable sets of words.
Hybrid continuous-discrete models naturally represent many real-world applications in robotics, finance, and environmental engineering. Inference with large-scale models is challenging because relational structures deteriorate rapidly during inference with observations. The main contribution of this paper is an efficie…
Modeling firm default with a variable threshold based on management decisions.
problem Estimating default probability with asymmetric information.
method Generalized structural model with a variable default threshold.
result The information level significantly impacts default probability and credit yield spread.
We present a new Markov chain Monte Carlo method for estimating posterior probabilities of structural features in Bayesian networks. The method draws samples from the posterior distribution of partial orders on the nodes; for each sampled partial order, the conditional probabilities of interest are computed exactly. We…
New method calculates tail probabilities of random vectors under linear transformations.
problem Computing tail probabilities of random vectors under linear transformations.
method Characterization of regular variation on cones in [0,∞)d under random linear transformations. result Allows computation of probabilities of tail events that were previously negligible.
We introduce a Bayesian approach to discovering patterns in structurally complex processes. The proposed method of Bayesian Structural Inference (BSI) relies on a set of candidate unifilar HMM (uHMM) topologies for inference of process structure from a data series. We employ a recently developed exact enumeration of to…
In recent years research on credit risk modelling has mainly focused on default probabilities. Recovery rates are usually modelled independently, quite often they are even assumed constant. Then, however, the structural connection between recovery rates and default probabilities is lost and the tails of the loss distri…
ChoiceRank learns network edge probabilities from node traffic data.
problem Learning edge transition probabilities from node-level traffic data.
method Preference learning model based on Luce's axiom, iterative algorithm.
result Successfully recovers edge transition probabilities from marginal node traffic data.
We combine Bayesian networks (BNs) and structural reliability methods (SRMs) to create a new computational framework, termed enhanced Bayesian network (eBN), for reliability and risk analysis of engineering structures and infrastructure. BNs are efficient in representing and evaluating complex probabilistic dependence …
Investigates statistical properties of perturb-softmax and perturb-argmax distributions.
problem Underexplored statistical properties of Gumbel-Softmax and Gumbel-Argmax distributions.
method Investigates convexity and differentiability to determine completeness and minimality of these distributions.
result Identifies parameters that admit complete and minimal representation of probability distributions.
SLM models code syntax as trees to generate any programming language code.
problem Generating any piece of code in a given language without restrictions.
method Structural language modeling (SLM) decomposes code into ASTs and estimates probabilities over nodes.
result SLM model generates arbitrary code in any language, outperforming previous methods.
A new metric based on hitting probabilities for directed graphs and Markov chains.
problem Lack of metrics specifically adapted to asymmetric structure of directed graphs and Markov chains.
method Metric based on hitting probabilities, insensitive to shortest and average walk distances.
result New structural theory of directed graphs and utility for various applications.
We show that the martingale component in the long-term factorization of the stochastic discount factor due to Alvarez and Jermann (2005) and Hansen and Scheinkman (2009) is highly volatile, produces a downward-sloping term structure of bond Sharpe ratios, and implies that the long bond is far from growth optimality. In…