Bayesian learning in undirected graphical models|computing posterior distributions over parameters and predictive quantities is exceptionally difficult. We conjecture that for general undirected models, there are no tractable MCMC (Markov Chain Monte Carlo) schemes giving the correct equilibrium distribution over param…
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48 results for “distribution over parameters”
Bayesian neural networks simplified with input augmentation.
problem Uncertainty in deep learning models.
method Layer-wise input augmentation to induce uncertainty distributions.
result State-of-the-art performance in uncertainty representation.
The paper proposes a method for better uncertainty estimation in neural networks.
problem Estimating predictive uncertainty in neural networks is crucial but challenging.
method The paper proposes a function-space variational inference method to infer a posterior distribution over functions.
result The proposed method leads to state-of-the-art uncertainty estimation and predictive performance.
A parsimonious model reduces over-parameterization in skewed matrix variate mixtures.
problem Over-parameterization in skewed matrix variate mixtures.
method Parsimonious family of 256 models using bilinear factor analyzers constrained over clusters, with AECM algorithm for estimation.
result Extensive simulations and real-world datasets (MNIST, Olivetti faces) demonstrate the method's effectiveness.
Study shows neural network parameters converge to ridgelet spectrum.
problem Characterization of local minima in over-parametrized neural networks.
method Developed ridgelet transform to analyze neural network parameters.
result Distribution of parameters converges to ridgelet spectrum.
A new meta-learning method using shared variational inference.
problem Meta-learning with uncertainty over model parameters.
method Shared amortized variational inference network for conditional prior and posterior.
result Prevents collapse of conditional prior to Dirac delta function.
In this paper we present decomposable priors, a family of priors over structure and parameters of tree belief nets for which Bayesian learning with complete observations is tractable, in the sense that the posterior is also decomposable and can be completely determined analytically in polynomial time. This follows from…
KOMET identifies Koopman operators from model parameter trajectories to adapt to evolving data distributions.
problem Adaptation of parametric models to non-stationary environments.
method Data-driven framework using Koopman operator identification and Extended Dynamic Mode Decomposition (EDMD).
result KOMET achieves high autonomous-rollout accuracies of 0.981 to 1.000 over 100 time steps on various drifting datasets.
Bayesian models that mix multiple Dirichlet prior parameters, called Multi-Dirichlet priors (MD) in this paper, are gaining popularity. Inferring mixing weights and parameters of mixed prior distributions seems tricky, as sums over Dirichlet parameters complicate the joint distribution of model parameters. This paper s…
Unified framework for optimizing portfolios with distributions over weights, returns, and parameters.
problem Traditional portfolio optimization treats expected returns, covariances, and allocations as fixed. Modern practice replaces at least one with a distribution.
method Unified framework using Gamma_theta(dw,dr) coupling to organize Bayesian, robust, chance-constrained, stochastic-allocation, and distributional reinforcement-learning methods.
result Synthetic and structural contributions, including a portfolio specialization of Wasserstein-CVaR duality and a static no-randomization theorem.
Paired estimation of change in parameters of interest over a population plays a central role in several application domains including those in the social sciences, epidemiology, medicine and biology. In these domains, the size of the population under study is often very large, however, the number of observations availa…
Joint Bayesian Inference of Graphical Structure and Parameters with a Single Generative Flow Networkcs.LG
A new method infers graph structure and parameters using a single generative flow network.
problem Bayesian Network structure and parameter inference from data.
method Single GFlowNet with two-phase sampling: DAG generation followed by parameter assignment.
result Accurate approximation of joint posterior distribution over graph structure and parameters.
Dense Distributions from Sparse Samples: Improved Gibbs Sampling Parameter Estimators for LDAstat.ML
We introduce a novel approach for estimating Latent Dirichlet Allocation (LDA) parameters from collapsed Gibbs samples (CGS), by leveraging the full conditional distributions over the latent variable assignments to efficiently average over multiple samples, for little more computational cost than drawing a single addit…
A defining feature of non-stationary systems is the time dependence of their statistical parameters. Measured time series may exhibit Gaussian statistics on short time horizons, due to the central limit theorem. The sample statistics for long time horizons, however, averages over the time-dependent parameters. To model…
New meta-learning framework for minimizing simple regret in bandits.
problem Minimizing simple regret in a sequence of bandit tasks with unknown distributions.
method Developed Bayesian and frequentist meta-learning algorithms for bandits, analyzing their meta simple regret.
result Bayesian algorithm achieves meta simple regret, frequentist algorithm .
Policy evaluation is a key process in reinforcement learning. It assesses a given policy using estimation of the corresponding value function. When using a parameterized function to approximate the value, it is common to optimize the set of parameters by minimizing the sum of squared Bellman Temporal Differences errors…
Method leverages population data to deconvolve unknown noise and model parameters.
problem Deconvolution of unknown observational noise in distributional inversion problems.
method Large data sets from physical systems, modified gradient descent, active learning.
result Simultaneous deconvolution of noise and model parameters.
We present a new family of exchangeable stochastic processes, the Functional Neural Processes (FNPs). FNPs model distributions over functions by learning a graph of dependencies on top of latent representations of the points in the given dataset. In doing so, they define a Bayesian model without explicitly positing a p…
Capital distribution curve is defined as log-log plot of normalized stock capitalizations ranked in descending order. The curve displays remarkable stability over periods of time. Theory of exchangeable distributions on set partitions, developed for purposes of mathematical genetics and recently applied in non-parametr…
Information-Geometric Optimization (IGO) is a unified framework of stochastic algorithms for optimization problems. Given a family of probability distributions, IGO turns the original optimization problem into a new maximization problem on the parameter space of the probability distributions. IGO updates the parameter …
The paper reinterprets Bayesian priors and posteriors using Riemannian manifolds.
problem The dependence of maximum a posteriori estimates on parametrization.
method Assuming a Riemannian manifold with Fisher metric, the paper reinterprets priors and posteriors as distributions over probability distributions, making estimates independent of parametrization.
result A maximum a posteriori estimate independent of parametrization is defined.
Study decomposes uncertainty in HK-distribution parameter estimation for QUS.
problem Uncertainty in HK-distribution parameter estimation for quantitative ultrasound.
method Bayesian Neural Networks (BNNs) for parameter estimation and uncertainty decomposition.
result Decomposes total predictive uncertainty into epistemic and aleatoric components.
This work models financial market returns with asymmetric Tsallis distributions, improving fit over symmetric q-Gaussians.
problem Non-symmetric behavior of stock market returns over time scales.
method Linear combination of two independent normalized half q-Gaussians with different parameters.
result Asymmetric distributions provide better fits to stock market returns than symmetric q-Gaussians, especially over longer time scales.
A fast method for estimating radar amplitude density parameters.
problem Accurate estimation of amplitude density function parameters in radar applications.
method Projecting amplitude data onto horizontal and vertical axes, then using MLE for -stale distribution parameters.
result The average of computed MLEs based on two projections is a fast and accurate estimator for amplitude distribution parameters.
This work tackles the challenge of Bayesian deep learning by proposing a new framework for matching Gaussian process priors with neural network parameters.
problem The challenge of specifying priors over neural network parameters, which affects the induced functional prior and is uncontrolled.
method The approach involves defining functional priors using Gaussian processes and matching these priors with the functional prior of neural networks through the minimization of Wasserstein distance.
result The proposed framework offers systematic performance improvements over alternative priors and approximate Bayesian deep learning approaches.
Bayesian optimization adapts domain parameters for more robust robot policies.
problem Learning policies for robot control from simulation data often fails in the real world due to the 'reality gap'.
method Bayesian Domain Randomization (BayRn) uses Bayesian optimization to adapt domain parameter distributions during training.
result BayRn achieves better sim-to-real transfer compared to fixed distribution methods.
We investigate an existing distributed algorithm for learning sparse signals or data over networks. The algorithm is iterative and exchanges intermediate estimates of a sparse signal over a network. This learning strategy using exchange of intermediate estimates over the network requires a limited communication overhea…
New method optimizes sensor placement for stochastic systems efficiently.
problem Optimizing sensor placements for black-box stochastic systems with computational constraints.
method Trains a joint energy-based model on simulation data to learn parameter and solution distributions, allowing efficient sensor placement.
result Demonstrates lower computational cost and more informative sensor locations compared to conventional approaches.
DSCOVR: Randomized Primal-Dual Block Coordinate Algorithms for Asynchronous Distributed Optimizationmath.OC
Machine learning with big data often involves large optimization models. For distributed optimization over a cluster of machines, frequent communication and synchronization of all model parameters (optimization variables) can be very costly. A promising solution is to use parameter servers to store different subsets of…
Paper improves parameter estimation of continuous distributions using preference feedback.
problem Improving parameter estimation of continuous distributions.
method Preference-based M-estimators and deterministic preferences.
result Preference-based estimators achieve an estimation error scaling of O(1/n), significantly faster than sample-only methods.
Bayesian uncertainty quantification is flawed, according to new research.
problem Flawed interpretation of Bayesian uncertainty quantification.
method Discussion of Bayesian updating and optimization-based perspective, proposing measures of quality.
result Bayesian uncertainty quantification is not coherent with optimization-based perspective.
Fixed-parameter tractability of private synthetic data generation
problem Generating synthetic data under differential privacy
method Linear programming and subsampled private multiplicative weights method
result Optimal error rates across all regimes
This work proposes a new method for variational inference using Wasserstein gradient descent.
problem Optimizing variational parameters to match a true posterior distribution.
method Reinterpreting VI as an optimization problem over a variational parameter space, using Wasserstein gradient descent.
result The proposed Wasserstein gradient descent can be seen as a generalization of existing optimization techniques in VI.
Singularity structures and impacts on parameter estimation in finite mixtures of distributionsmath.ST
Singularities of a statistical model are the elements of the model's parameter space which make the corresponding Fisher information matrix degenerate. These are the points for which estimation techniques such as the maximum likelihood estimator and standard Bayesian procedures do not admit the root- parametric rate…
We show that the only parameter prior for complete Gaussian DAG models that satisfies global parameter independence, complete model equivalence, and some weak regularity assumptions, is the normal-Wishart distribution. Our analysis is based on the following new characterization of the Wishart distribution: let W be an …
Mechanistic models of single-neuron dynamics have been extensively studied in computational neuroscience. However, identifying which models can quantitatively reproduce empirically measured data has been challenging. We propose to overcome this limitation by using likelihood-free inference approaches (also known as App…
The paper analyzes optimal implicit bias in linear regression for over-parameterized models.
problem Finding the best generalization performance in over-parameterized linear regression.
method Asymptotic analysis of generalization performance for convex functions/potentials.
result Optimal implicit bias that achieves the best generalization error under certain conditions.
Current methods for learning graphical models with latent variables and a fixed structure estimate optimal values for the model parameters. Whereas this approach usually produces overfitting and suboptimal generalization performance, carrying out the Bayesian program of computing the full posterior distributions over t…
Gradient matching with Gaussian processes is a promising tool for learning parameters of ordinary differential equations (ODE's). The essence of gradient matching is to model the prior over state variables as a Gaussian process which implies that the joint distribution given the ODE's and GP kernels is also Gaussian di…
This paper considers a simulation-based estimator for a general class of Markovian processes and explores some strong consistency properties of the estimator. The estimation problem is defined over a continuum of invariant distributions indexed by a vector of parameters. A key step in the method of proof is to show the…
We present a distributed (non-Bayesian) learning algorithm for the problem of parameter estimation with Gaussian noise. The algorithm is expressed as explicit updates on the parameters of the Gaussian beliefs (i.e. means and precision). We show a convergence rate of with the constant term depending on the numb…
Researchers prove NP-hardness of learning parameter-bounded Bayes nets.
problem Learning parameter-bounded Bayes nets is computationally hard.
method Proved NP-hardness of learning parameter-bounded Bayes nets and a promise search variant.
result Proved NP-hardness of a promise search variant of LEARN.
OPNP prunes parameters and neurons to improve OOD detection without training.
problem Detecting out-of-distribution samples in real-world machine learning models.
method OPNP approach that identifies and removes sensitive parameters and neurons.
result OPNP consistently outperforms existing methods on multiple OOD detection tasks.
PostNet predicts uncertainty without OOD data, improving OOD detection and calibration.
problem Accurate uncertainty estimation for safe systems.
method PostNet uses Normalizing Flows to learn individual posterior distributions over predicted probabilities.
result PostNet achieves state-of-the-art results in OOD detection and uncertainty calibration.
Deep Priorstat.ML
The recent literature on deep learning offers new tools to learn a rich probability distribution over high dimensional data such as images or sounds. In this work we investigate the possibility of learning the prior distribution over neural network parameters using such tools. Our resulting variational Bayes algorithm …
Rethinking Test-Time Training: Tilting The Latent Distribution For Few-Shot Source-Free Adaptationstat.ML
Method adapts frozen models for few-shot tasks without training.
problem Deployment constraints limit model updates, necessitating new adaptation methods.
method Exponential tilting of latent distribution for inference.
result Method outperforms parameter-update methods across benchmarks.
Improved learning of probabilistic box embeddings by modeling parameters with Gumbel distributions.
problem Local identifiability issues in geometric embeddings.
method Modeling box parameters with min and max Gumbel distributions, calculating expected intersection volume.
result Improves the ability of probabilistic box embeddings to learn.
Dirichlet pruning compresses neural networks by removing unimportant units.
problem Compressing large neural network models without sacrificing performance.
method Assigns Dirichlet distribution over network layers' units and uses variational inference to estimate parameters.
result Achieves state-of-the-art compression performance on larger architectures like VGG and ResNet.