DNAF accelerates DQL for efficient resource allocation in network slicing.
problem Efficient resource allocation in network slicing with varying demands.
method Introduced discrete normalized advantage functions (DNAF) into DQL, using a k-nearest neighbor algorithm for discrete action space.
result DNAF-based DQL converges faster through simulations.
DIF extends NF with stochastic discrete latent variables for better density estimation.
problem Improving density estimation with discontinuities and fine details.
method Discretely indexed flows as an extension of Normalizing Flows with stochastic latent variables.
result DIF inherit good computational behavior of NF and can capture distributions with discontinuities.
The paper analyzes the randomized midpoint method for Langevin diffusions, revealing biases and asymptotic properties.
problem Analyzing biases and asymptotic properties of the randomized midpoint method for Langevin diffusions.
method Characterization of stationary distribution and asymptotic normality for numerical integration.
result The step-size needs to go to zero for the method to be asymptotically unbiased.
This paper puts forth a new formulation and algorithm for the elastic matching problem on unparametrized curves and surfaces. Our approach combines the frameworks of square root normal fields and varifold fidelity metrics into a novel framework, which has several potential advantages over previous works. First, our var…
Improved RCPs for MABs using normalized weight functions.
problem Slow convergence and inferior rewards in RCPs for MABs.
method Generalized marginalization of rewards using normalized weight functions.
result Improved RCPs become competitive with classic methods.
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.
A new method reparameterizes Gaussian noise for better flexibility and performance.
problem Improving the Gumbel-Softmax for better flexibility and performance.
method Invertible Gaussian Reparameterization (IGR) using modified softmax and transformations.
result IGR outperforms Gumbel-Softmax in various experiments.
The paper develops approximations for Pearson's chi-square statistic and applies them to confidence intervals.
problem Finding confidence intervals for strictly convex functions of discrete distribution weights.
method Non-asymptotic local normal approximation for multinomial probabilities, deriving bounds and coupling inequalities.
result Developed methods to find confidence intervals for negative entropy of discrete distributions.
A new method for discrete data normalizing flows using latent transformations.
problem Challenges in parameterizing bijective transformations for discrete data.
method Predict a distribution over latent transformations to make the marginal likelihood differentiable.
result Discrete-data normalizing flows can be trained using gradient-based learning with unbiased score function estimation.
Inspired by the Weierstrass representation of smooth affine minimal surfaces with indefinite metric, we propose a constructive process producing a large class of discrete surfaces that we call discrete affine minimal surfaces. We show that they are critical points of an affine area functional defined on the space of qu…
simpcomp is an extension to GAP, the well known system for computational discrete algebra. It allows the user to work with simplicial complexes. In the latest version, support for simplicial blowups and discrete normal surfaces was added, both features unique to simpcomp. Furthermore, new functions for constructing cer…
New algorithm learns value and advantage functions for continuous-time Markov processes without structural assumptions.
problem Learning value and advantage functions for continuous-time Markov processes without structural assumptions.
method Proposes Sobolev-prox fitted q-learning algorithm based on Hilbert-space positive definiteness and boundedness properties of Bellman operators. result Identifies ellipticity as a key structural property enabling reinforcement learning for Markov diffusions.
Improves NF for complex data distributions with multiple modes.
problem Difficulty in handling data distributions with multiple isolated modes.
method Proposes a new framework using variational latent representation to improve NF.
result Significantly more powerful for generating data distributions with multiple modes.
In this paper the Buchen's pricing formulae of (higher order) asset and bond binary options are incorporated into the pricing formula of power binary options and a pricing formula of "the normal distribution standard options" with the maturity payoff related to a power function and the density function of normal distri…
Flow based models such as Real NVP are an extremely powerful approach to density estimation. However, existing flow based models are restricted to transforming continuous densities over a continuous input space into similarly continuous distributions over continuous latent variables. This makes them poorly suited for m…
Paper develops Bayesian inference for discrete-choice mnp models with Gaussian priors.
problem Estimating parameters of discrete-choice multinomial probit models with Gaussian priors.
method Adapts Fasano and Durante's results to a specific mnp model with zero mean and independent Gaussian priors, simplifying posterior distribution parameters and providing a new variational algorithm.
result Simplified expressions for posterior distribution parameters and a novel variational algorithm.
SGD converges to critical points of normalized margin in late-stage training for homogeneous neural networks.
problem Analyzing the implicit bias of SGD on homogeneous neural networks.
method Interpreting SGD dynamics as an Euler-like discretization of a conservative field flow associated with the normalized classification margin.
result Normalized SGD iterates converge to the set of critical points of the normalized margin at late-stage training.
We find a normal form for two-input flat discrete-time systems.
problem No comparable normal form exists for flat continuous-time systems.
method State- and input transformations to achieve a triangular structure.
result A systematic parameterization of system variables by the flat output and its shifts.
Woodbury transformations improve deep generative models with efficient invertibility and determinant calculation.
problem Efficiently invertible and determinant-calculable functions for deep generative models.
method Introducing Woodbury transformations that leverage matrix identities for efficient invertibility and determinant calculation.
result Woodbury transformations enable high-dimensional interactions, efficient sampling, and likelihood evaluation, outperforming other flow architectures.
New discrete-time model shows insider trading dynamics.
problem Modeling insider trading with discrete time and noise traders.
method Formulated as a game with three types of traders, including an insider, noise traders, and a market maker. Proved existence of sequential Kyle equilibrium for various distributions and information flows.
result Equilibria exist in mixed strategies but not in pure strategies, unlike in Kyle's original model.
Arguably, the two most popular accelerated or momentum-based optimization methods in machine learning are Nesterov's accelerated gradient and Polyaks's heavy ball, both corresponding to different discretizations of a particular second order differential equation with friction. Such connections with continuous-time dyna…
Proposes a continuous relaxation for discrete Bayesian optimization.
problem Efficiently optimizing discrete data with limited target observations.
method Continuous relaxation of objective function, incorporating prior knowledge.
result Optimization can be computationally tractable with few observations.
The parameter estimation of unnormalized models is a challenging problem. The maximum likelihood estimation (MLE) is computationally infeasible for these models since normalizing constants are not explicitly calculated. Although some consistent estimators have been proposed earlier, the problem of statistical efficienc…
TriTPP models enable faster and more flexible event data modeling.
problem Inflexibility and slow sampling in traditional TPP models.
method Triangular Maps and Normalizing Flows for parallel sampling and likelihood computation.
result TriTPP models achieve orders of magnitude faster sampling while maintaining flexibility.
A new method for categorical variational inference using discrete normalizing flows.
problem Challenges in optimizing variational approximations for discrete latent variables.
method Differentiable reparameterization using a mixture of discrete normalizing flows.
result Improves optimization of evidence lower bound and reduces sensitivity to hyperparameters.
A new method uses normalizing flows to approximate optimal transport between empirical distributions.
problem Learning an optimal transport map between two empirical distributions.
method Relaxing the Monge formulation of optimal transport, using normalizing flows to approximate the solution.
result The method provides a good approximation of the true optimal transport.
Discrete flows extend normalizing flows to discrete data, improving various applications.
problem Applying normalizing flows to discrete data distributions.
method Developed discrete autoregressive and bipartite flows, showing their effectiveness on various discrete data tasks.
result Discrete autoregressive flows outperform autoregressive baselines on synthetic discrete distributions and Potts models.
Normalizing flows are a powerful class of generative models for continuous random variables, showing both strong model flexibility and the potential for non-autoregressive generation. These benefits are also desired when modeling discrete random variables such as text, but directly applying normalizing flows to discret…
New method for mesh denoising using TGV of normal vector field.
problem Improving mesh quality by removing noise.
method Proposes a novel TGV formulation for normal vector fields on triangular meshes.
result New method outperforms existing techniques in mesh denoising experiments.
We describe discrete restricted Boltzmann machines: probabilistic graphical models with bipartite interactions between visible and hidden discrete variables. Examples are binary restricted Boltzmann machines and discrete naive Bayes models. We detail the inference functions and distributed representations arising in th…
New method learns disentangled discrete representations using categorical variational autoencoders.
problem Learning disentangled representations from discrete latent spaces.
method Replaced standard Gaussian VAE with a categorical VAE to mitigate rotational invariance.
result Categorical distributions improve learning of disentangled representations.
Ubiquitous anomalies endanger the security of our system constantly. They may bring irreversible damages to the system and cause leakage of privacy. Thus, it is of vital importance to promptly detect these anomalies. Traditional supervised methods such as Decision Trees and Support Vector Machine (SVM) are used to clas…
Asymptotic net is an important concept in discrete differential geometry. In this paper, we show that we can associate affine discrete geometric concepts to an arbitrary non-degenerate asymptotic net. These concepts include discrete affine area, mean curvature, normal and co-normal vector fields and cubic form, and the…
The paper shows commensurators of certain subgroups are discrete.
problem Understanding commensurators of specific subgroups in Lie groups.
method Analyzing commensurators of thin normal subgroups with abelian quotients.
result The commensurator of certain subgroups is discrete.
Study answers arithmeticity question for normal subgroup of lattices.
problem Arithmeticity of discrete subgroups of semisimple Lie groups with dense commensurators.
method Examined normal subgroups of lattices in semisimple Lie groups.
result Positive answer to Greenberg-Shalom's question for lattices.
TROLL improves RL for LLMs by replacing clipping with a trust region projection.
problem Clipping in RL for LLMs causes instability and suboptimal performance.
method TROLL uses a discrete differentiable trust region projection to replace clipping, balancing computational cost and effectiveness.
result TROLL consistently outperforms PPO-like clipping in training speed, stability, and final success rates.
The study classifies discrete pseudomanifolds with up to 2d+7 vertices.
problem Understanding discrete pseudomanifolds with a small number of vertices.
method Proved existence of at least 2(d+1) vertices, classified up to 2d+6 vertices, established equivalence with edge graphs of flag normal pseudomanifolds.
result Every flag normal d-pseudomanifold with at most 2d+7 vertices is either a simplicial d-sphere or a flag triangulation of the (d-2)-fold suspension of RP^2.
Paper proposes a new generative model for discrete distributions using flows on submanifolds.
problem Discretization issues and complex statistical dependencies in discrete data.
method Continuous normalizing flows on factorizing discrete measures, geodesic flow matching.
result Efficient training and broad applicability demonstrated through experiments.
Discrete normal surfaces are normal surfaces whose intersection with each tetrahedron of a triangulation has at most one component. They are also natural Poincaré duals to 1-cocycles with $\ZZ/2\ZZ$-coefficients. For a fixed cohomology class in a simplicial poset the average Euler characteristic of the associated discr…
Study shows how insurance processes converge to a specific model for better ruin probability calculations.
problem Calculating ruin probabilities in insurance processes.
method Proved convergence of insurance processes to a generalized Ornstein-Uhlenbeck process, derived approximations for ruin probabilities.
result Discrete-time insurance surplus processes converge weakly to a generalized Ornstein-Uhlenbeck process, providing insights for ruin theory.
Discrete diffusion models improve data generation for discrete data like language and graphs.
problem Adapting diffusion models to discrete state spaces for better data generation.
method Formulated as CTMCs, used uniformization of continuous Markov chains for sampling.
result Derive guarantees for sampling from any distribution on a hypercube, aligning with state-of-the-art achievements.
Library learns Bayesian networks from mixed data without discretization.
problem Learning Bayesian networks from mixed data (discrete and continuous variables).
method Proposes an algorithm for structural and parameter learning of Bayesian networks from mixed data using a mixed MI score function and Gaussian approximation. Offers two graph structure enumeration algorithms.
result Advantages in solving approximation and gap recovery problems on synthetic and real datasets.
We derive the exact solution of a one-dimensional Markov functional model with log-normally distributed interest rates in discrete time. The model is shown to have two distinct limiting states, corresponding to small and asymptotically large volatilities, respectively. These volatility regimes are separated by a phase …
New method combines value function decomposition and policy gradients for cooperative multi-agent reinforcement learning.
problem Challenges in cooperative multi-agent reinforcement learning, especially credit assignment and large action spaces.
method Decomposed Soft Actor-Critic (mSAC) method with Q network architecture, discrete probabilistic policy, and counterfactual advantage function.
result Significantly outperforms policy-based approach COMA and achieves competitive results with SOTA value-based approach Qmix.
We present sparse topical coding (STC), a non-probabilistic formulation of topic models for discovering latent representations of large collections of data. Unlike probabilistic topic models, STC relaxes the normalization constraint of admixture proportions and the constraint of defining a normalized likelihood functio…
Principal component analysis (PCA) is arguably the most popular tool in multivariate exploratory data analysis. In this paper, we consider the question of how to handle heterogeneous variables that include continuous, binary, and ordinal. In the probabilistic interpretation of low-rank PCA, the data has a normal multiv…
We propose a novel time discretization for the log-normal SABR model and derive its asymptotic properties.
problem Analyzing the log-normal SABR model's time-discretized behavior and implied volatility surface.
method We use the Euler-Maruyama scheme for time discretization and derive asymptotic properties in the limit of large number of time steps.
result We derive an exact representation of the implied volatility surface for arbitrary maturity and strike in the asymptotic regime.
Let E be the Engel group and D be a rank 2 bracket generating left invariant distribution with a Lorentzian metric, which is a nondegenerate metric of index 1. In this paper, we first prove that timelike normal extremals are locally maximizing. Second, we obtain a parametrization of timelike, spacelike, lightlike norma…