This paper presents a new approach, called perturb-max, for high-dimensional statistical inference that is based on applying random perturbations followed by optimization. This framework injects randomness to maximum a-posteriori (MAP) predictors by randomly perturbing the potential function for the input. A classic re…
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48 results for “Max A Posteriori”
Observations depending on sums of random variables are common throughout many fields; however, no efficient solution is currently known for performing max-product inference on these sums of general discrete distributions (max-product inference can be used to obtain maximum a posteriori estimates). The limiting step to …
The maximum a posteriori (MAP) configuration of binary variable models with submodular graph-structured energy functions can be found efficiently and exactly by graph cuts. Max-product belief propagation (MP) has been shown to be suboptimal on this class of energy functions by a canonical counterexample where MP conver…
In this paper we relate the partition function to the max-statistics of random variables. In particular, we provide a novel framework for approximating and bounding the partition function using MAP inference on randomly perturbed models. As a result, we can use efficient MAP solvers such as graph-cuts to evaluate the c…
Bayesian CycleGAN improves cycle-consistent GANs by stabilizing training and diversifying generated images.
problem Challenges in stabilizing training of cycle-consistent GANs leading to mode collapse.
method Proposes a Bayesian approach to stabilize training and diversify generated images.
result Improves per-pixel accuracy by 15% on Cityscapes semantic segmentation task and 20% on Monet2Photo style transfer.
PMP improves sampling and learning in complex energy models.
problem Intractability of MAP computation in EBMs.
method Perturb-and-max-product (PMP) for parallel and scalable sampling and learning.
result PMP outperforms existing methods in various models, including Ising and RBMs.
The paper parallelizes HMM inference for efficient long-term computations.
problem Efficiently computing inference in long-term hidden Markov models.
method Parallelization using associative elements and operators for sum-product and max-product algorithms.
result The proposed parallel algorithms are computationally efficient for long time horizons.
Bayesian approach improves ODE solution accuracy.
problem Improving numerical solutions of ordinary differential equations.
method Bayesian inference with Gaussian filtering and smoothing.
result Maximum a posteriori estimate converges to true solution at polynomial rate.
We introduce an approximate search algorithm for fast maximum a posteriori probability estimation in probabilistic programs, which we call Bayesian ascent Monte Carlo (BaMC). Probabilistic programs represent probabilistic models with varying number of mutually dependent finite, countable, and continuous random variable…
Inspired by trading, this method segments time series efficiently.
problem Time series segmentation for multivariate data.
method Normalize time series, treat each channel as a stock, use a posteriori trading signals for segmentation.
result Proposed method is faster and produces more intuitive results than existing models.
A Posteriori Error Estimator for a Front-Fixing Finite Difference Scheme for American Optionsq-fin.MF
For the numerical solution of the American option valuation problem, we provide a script written in MATLAB implementing an explicit finite difference scheme. Our main contribute is the definition of a posteriori error estimator for the American options pricing which is based on Richardson's extrapolation theory. This e…
Max-product Belief Propagation (BP) is a popular message-passing algorithm for computing a Maximum-A-Posteriori (MAP) assignment over a distribution represented by a Graphical Model (GM). It has been shown that BP can solve a number of combinatorial optimization problems including minimum weight matching, shortest path…
The marginal maximum a posteriori probability (MAP) estimation problem, which calculates the mode of the marginal posterior distribution of a subset of variables with the remaining variables marginalized, is an important inference problem in many models, such as those with hidden variables or uncertain parameters. Unfo…
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.
We solve image inverse problems using a flow-based noise model.
problem Image inverse problems with complex noise patterns.
method Normalizing flow prior for maximum a posteriori estimation.
result Empirical validation on various inverse problems.
Study introduces statistical mechanics for min-max problems.
problem Understanding the properties of min-max problems in high dimensions.
method Statistical mechanical formalism for analyzing min-max problems.
result Derives the relationship between training data and generalization error.
Study shows strong min-max principle for phase transitions.
problem Understanding nodal sets near minimal hypersurfaces.
method Analogous to White's principle, applies to Allen-Cahn energy.
result Strong min-max principle for phase transitions.
Equity-Transformer solves NP-hard min-max routing problems efficiently.
problem Min-max routing problems with multiple agents and large-scale applications.
method Sequential planning approach with Transformer and equitable workload distribution inductive biases.
result Significant runtime and cost reductions in min-max mTSP and min-max mPDP tasks.
Study max- and min-stability under first-order stochastic dominance, finding new functional characterizations.
problem Understanding max- and min-stability in stochastic dominance.
method Representation theorem for functionals satisfying max-stability, combining max- and min-stability to define Lambda-quantiles.
result New characterizations of functionals, including Lambda-quantiles, in finance and political science.
Max-min margin Markov networks improve consistency in structured prediction.
problem Statistical inconsistency in max-margin methods for structured prediction.
method Defining a max-min margin formulation to overcome statistical inconsistency.
result Proves consistency and provides an explicit algorithm with finite sample generalization bounds.
Upper bound for Morse index of min-max varifolds.
problem Bounding Morse index of varifolds.
method Proving upper bound for Morse index of min-max stationary integral varifolds.
result Upper bound for Morse index of min-max stationary integral varifolds.
Upper bound for max-sliced 2-Wasserstein distance between measures.
problem Estimating distance between probability measures and their empirical counterparts.
method Same technique as previous work, upper bound approach.
result Upper bound for expected max-sliced 2-Wasserstein distance.
Estimates parameters in max-linear Bayesian networks with noise.
problem Causal inference in extreme-value settings with noise parameters.
method Max-plus algebra and logarithm transformation, normal distribution estimation, EM algorithm and quadratic optimization.
result An estimator of a parameter for each edge in a DAG is normally distributed.
Localized min-max method proves minimal hypersurface existence.
problem Existence of minimal hypersurfaces in complete manifolds.
method Localized min-max approach to prove existence.
result Existence of complete embedded minimal hypersurface with index at most one.
The paper solves min-max widths on a 3-sphere and strengthens multiplicity theorems.
problem Which min-max widths of the unit 3-sphere lie between and ?
method Homological min-max theory and stronger versions of multiplicity one theorems.
result Proves the 10th to 13th min-max widths of the unit 3-sphere lie between and .
Proves multiplicity one for min-max minimal hypersurfaces in specific manifolds.
problem Proving multiplicity one for min-max minimal hypersurfaces in specific manifolds.
method Using min-max theory for hypersurfaces with prescribed mean curvature and approximating min-max values.
result Confirms a conjecture by Marques-Neves for min-max minimal hypersurfaces in bumpy metrics.
Characterizes Zoll metrics via min-max values.
problem Characterizing Zoll Riemannian metrics.
method Uses min-max values in a loop space.
result Two min-max values coincide for Zoll metrics.
LS-SVR and Bayesian RBF networks are shown to be theoretically similar.
problem Improving LS-SVR performance through Bayesian methods.
method Formal demonstration of theoretical similarities between LS-SVR and Bayesian RBF networks.
result LS-SVR and Bayesian RBF networks have equivalent theoretical expressions.
Max flow/min cut theorem extended to currents and topology.
problem Continuous max flow/min cut theorem for complex domains.
method Continuous analogue of max flow/min cut theorem considering topology.
result Continuous max flow/min cut theorem proven for currents and laminations.
Paper corrects Max-Margin loss for multi-label tasks.
problem Max-Margin loss inconsistency in multi-label classification.
method Introduced Restricted-Max-Margin loss.
result Consistent loss for multi-label tasks under milder conditions.
Study how noisy labels affect semi-supervised learning.
problem Effect of noisy labels on semi-supervised learning performance.
method Proposed an algorithm derived from a continuous relaxation of the Maximum A Posteriori (MAP) estimator for a Degree Corrected Stochastic Block Model (DC-SBM).
result Our approach achieves promising performance even with very noisy labeled data.
Adaptive momentum method solves non-convex min-max problems.
problem Non-convex min-max optimization problems in training generative adversarial networks.
method Proposes an adaptive momentum algorithm for non-convex min-max optimization.
result Establishes non-asymptotic convergence rates for the proposed algorithm.
Paper proves finiteness and Morse index estimates for equivariant min-max hypersurfaces.
problem Existence and finiteness of -invariant minimal hypersurfaces.
method Equivariant min-max theory, compactness theorem, bumpy metrics theorem.
result Generalization of Morse index estimates to equivariant setting.
A posteriori multi-stage optimal trading under transaction costs and a diversification constraintq-fin.PM
This paper presents a simple method for a posteriori (historical) multi-variate multi-stage optimal trading under transaction costs and a diversification constraint. Starting from a given amount of money in some currency, we analyze the stage-wise optimal allocation over a time horizon with potential investments in mul…
New findings cast doubt on the role of in generalizing neural networks.
problem The role of in neural network generalization remains unclear.
method Experiments with various training interventions and batch sizes.
result Generalization benefits can vanish at larger batch sizes, challenging the role of .
New proof of Smale conjecture for RP^3 and lens spaces using min-max theory.
problem Proving the Smale conjecture for specific spaces.
method Minimal surfaces and min-max theory.
result New proof of Smale conjecture for and lens spaces.
New method for MAP inference using Benders' decomposition.
problem Finite-time convergence guarantee for MAP inference.
method Sequentially adding constraints using Benders' decomposition.
result Higher optimal posterior value compared to other methods.
Paper improves Morse index bound for hypersurfaces.
problem Improving Morse index bound for hypersurfaces.
method Construction of hierarchical deformations and restrictive min-max theory.
result Generalizes a result by X. Zhou for .
New methods solve min-max problems on manifolds using Riemannian Hamiltonians.
problem Min-max optimization on Riemannian manifolds.
method Riemannian Hamiltonian methods (RHM) to minimize the Hamiltonian function.
result RHM leads to correct search directions and global optimality in min-max problems.
Tropical Geometry and Piecewise-Linear Approximation of Curves and Surfaces on Weighted Latticescs.LG
Tropical geometry and weighted lattices improve curve and surface fitting.
problem Fitting max- tropical curves and surfaces to data.
method Max- algebra, weighted lattices, morphological adjunctions.
result Optimal piecewise-linear regression for max- curves and surfaces.
Max-plus operators improve neural network filter selection and pruning.
problem Improving neural network efficiency and reducing redundancy.
method Exploiting Max-plus operators in neural network layers for filter selection and model pruning.
result Max-plus layers enhance filter selection and reduce redundancy without performance loss.
Bound on equivariant index for min-max surfaces.
problem Bounding the index of equivariant min-max surfaces.
method Equivariant min-max procedure with group action.
result Equivariant index bound by number of parameters.
Study MAP estimation for PnP priors with SGD, proving convergence and demonstrating practical applications.
problem Theoretical analysis and practical implementation of PnP priors for Bayesian imaging problems.
method Maximum-a-posteriori estimation with Plug & Play priors and stochastic gradient descent.
result Convergence proof for MAP computation by PnP-SGD under realistic assumptions on the denoiser.
Survey of advances in non-convex min-max optimization for applications.
problem Finding optimal solutions in non-convex, non-concave min-max problems.
method Selective review of theoretical and algorithmic advances.
result Exciting recent advances in solving non-convex min-max problems.
Max-affine regression method converges linearly using GD and SGD.
problem Regression of max-affine models in signal processing and statistics.
method Gradient descent and mini-batch stochastic gradient descent analysis.
result GD and SGD converge linearly to a neighborhood of the ground truth under sub-Gaussian assumptions.
New taxonomy and improved solvers for discrete energy minimization.
problem Maximum-a-posteriori inference in discrete graphical models.
method Dual block-coordinate ascent rule, theoretical analysis, new solver variants.
result Improved state-of-the-art solver outperforming existing methods on all test instances.
We reformulate LIPs as min-max problems for easier solution.
problem Recovering signals from few linear measurements.
method Proposed a min-max reformulation of LIPs.
result Saddle points characterize solutions to LIPs.
Max-Pooling Loss Training of Long Short-Term Memory Networks for Small-Footprint Keyword Spottingcs.CL
We propose a max-pooling based loss function for training Long Short-Term Memory (LSTM) networks for small-footprint keyword spotting (KWS), with low CPU, memory, and latency requirements. The max-pooling loss training can be further guided by initializing with a cross-entropy loss trained network. A posterior smoothin…