This work improves likelihood of score-based diffusion ODEs using high-order denoising score matching.
problem The gap between maximum likelihood and score matching objectives for score-based diffusion ODEs.
method High-order denoising score matching to maximize likelihood.
result Score-based diffusion ODEs achieve better likelihood on synthetic and CIFAR-10 data.
Generalizes moment-matching for exponential families with conditioning or hidden data.
problem Generalizing moment-matching conditions for exponential families with conditioning or hidden data.
method First-principles explanation and self-contained derivation of generalized moment-matching conditions.
result Derives generalized moment-matching conditions for conditional exponential families and hidden data.
Neural execution solves complex graph problems like bipartite matching.
problem Solving complex graph algorithms like maximum bipartite matching.
method Reduces bipartite matching to a flow problem and uses Ford-Fulkerson for maximum flow.
result Neural network achieves optimal matching almost 100% of the time.
Score matching offers efficient estimation for certain distributions.
problem Estimating probability distributions with intractable constants.
method Score matching as an alternative to maximum likelihood.
result Score matching is computationally and statistically efficient for certain distributions.
The well known maximum-entropy principle due to Jaynes, which states that given mean parameters, the maximum entropy distribution matching them is in an exponential family, has been very popular in machine learning due to its "Occam's razor" interpretation. Unfortunately, calculating the potentials in the maximum-entro…
DDSME outperforms SME in estimating multimodal distributions.
problem Efficiency of score matching in multimodal distributions.
method Diffusion-based denoising score matching (DDSME) compared to vanilla score matching (SME).
result DDSME avoids the error bound deterioration of SME with increasing mode separation.
Score matching fails for general point processes, a new estimator improves accuracy.
problem Score matching estimators fail for general point processes.
method Introduced a weighted score matching estimator for point processes.
result The weighted score matching estimator accurately estimates model parameters on synthetic and real data.
DFM simplifies CNF training without interpolants.
problem Efficiently training CNFs with computationally expensive ODE solving.
method DFM optimizes dual vector fields for bijective transformations.
result DFM outperforms CNF trained with FM or ML objectives.
Score matching is a recently developed parameter learning method that is particularly effective to complicated high dimensional density models with intractable partition functions. In this paper, we study two issues that have not been completely resolved for score matching. First, we provide a formal link between maxim…
We give polynomial-time algorithms for the exact computation of lowest-energy (ground) states, worst margin violators, log partition functions, and marginal edge probabilities in certain binary undirected graphical models. Our approach provides an interesting alternative to the well-known graph cut paradigm in that it …
New MMD estimators detect differences in missing paired data.
problem Handling missing data in matched pairs with complex distributions.
method Maximum mean discrepancy (MMD) estimators for complex data with missing values.
result Valid and consistent estimators detect differences in data distributions.
Given a pair of graphs with the same number of vertices, the inexact graph matching problem consists in finding a correspondence between the vertices of these graphs that minimizes the total number of induced edge disagreements. We study this problem from a statistical framework in which one of the graphs is an errorfu…
It is widely believed that learning good representations is one of the main reasons for the success of deep neural networks. Although highly intuitive, there is a lack of theory and systematic approach quantitatively characterizing what representations do deep neural networks learn. In this work, we move a tiny step to…
Maximum likelihood training improves the performance of score-based diffusion models.
problem Training score-based diffusion models with maximum likelihood.
method Trained by minimizing a weighted combination of score matching losses, with a specific weighting scheme that bounds negative log-likelihood.
result Maximum likelihood training improves the log-likelihood of score-based diffusion models across multiple datasets.
Score matching efficiency tied to distribution isoperimetric properties.
problem Understanding when score matching is as efficient as maximum likelihood.
method Connecting score matching efficiency to isoperimetric constants of distributions.
result Score matching is statistically efficient when the distribution has a small isoperimetric constant.
The paper models market dynamics using a limit order book system to explain slippage and inefficiency.
problem Inefficiency in matching markets due to structural liquidity constraints and slippage.
method Introduces a market microstructure framework with a latent preference state matrix and a dynamic discrete choice execution model.
result Persistent slippage and regional invariance of preference orderings are explained by liquidity thresholds.
Score matching fails to train VAEs robustly, revealing autoencoding loss insights.
problem Catastrophic failure of variational score matching on VAE models.
method Analysis of existing variational score matching objectives and their equivalence to autoencoding losses.
result Score matching methods fail to produce robust VAE models, predicting poor performance.
Motivated by the work of Salvetti and Settepanella we introduce certain total orderings of the faces of any shellable regular CW-complex (called `shelling-type orderings') that can be used to explicitly construct maximum acyclic matchings of the poset of cells of the given complex. Building on an application of this me…
This paper tackles matching two complete graphs with correlated edge weights in geometric models.
problem Matching two complete graphs with edge weights correlated through latent geometries.
method Derives an approximate maximum likelihood estimator for recovering hidden vertex correspondence.
result The estimator provably achieves perfect recovery under certain noise conditions.
Study connects database alignment and planted matching using Gaussian features.
problem Identify matching between correlated user features in anonymized databases.
method Derived results for database alignment and planted matching, showing connections and thresholds.
result Performance thresholds for database alignment converge to planted matching when feature dimensionality is sufficiently high.
The Maximum Mutual Information (MMI) criterion is different from the Least Error Rate (LER) criterion. It can reduce failing to report small probability events. This paper introduces the Channels Matching (CM) algorithm for the MMI classifications of unseen instances. It also introduces some semantic information method…
Matching correlated VAR time series databases by recovering matching permutations.
problem Matching perturbed and permuted correlated VAR time series.
method Probabilistic framework modeling, maximum likelihood estimator (MLE), linear assignment, convex relaxations.
result Recovery guarantees for perfect or partial recovery of matching permutations, thresholds for σ. Unified theory for causal inference using various methods.
problem Estimating causal effects in ATE estimation.
method Riesz regression, covariate balancing, DRE, TMLE, matching estimator.
result Unified theory integrating multiple methods for ATE estimation.
Paper tackles model vulnerabilities by reconstructing training data.
problem Reconstructing training data from model parameters poses a security risk.
method Developed a mathematical framework and score matching method for both Bayesian and non-Bayesian models.
result First score matching framework for reconstructing data in Bayesian models.
In this work we study the degree distribution, the maximum vertex and edge flow in non-uniform random Delaunay triangulations when geodesic routing is used. We also investigate the vertex and edge flow in Erdös-Renyi random graphs, geometric random graphs, expanders and random k-regular graphs. Moreover we show that …
New efficient algorithm for approximate PML distribution.
problem Computing the profile maximum likelihood (PML) distribution efficiently.
method Exploiting sparsity structure and new matrix rounding algorithm.
result First provable computationally efficient implementation of PseudoPML.
Score matching method improves density estimation for truncated data on manifolds.
problem Density estimation for truncated data on manifolds with intractable normalising constant.
method Truncated score matching extended to Riemannian manifolds with boundary.
result Score matching estimator approximates true parameter values with low error.
New method trains energy-based models faster and more stably.
problem Training efficiency and stability of energy-based models.
method EBFlow with score-matching objectives.
result EBFlow achieves significant speedup and better performance.
New bounds for score matching in polynomial exponential families.
problem Understanding the sample complexity of score matching for polynomial exponential families.
method Non-asymptotic sample complexity analysis for score matching.
result First finite sample bounds for score matching in polynomial exponential families.
Improves deep learning training by matching mini-batch distributions.
problem Overfitting and noise in mini-batch training.
method ITDM, which matches the moments of mini-batch distributions to reduce overfitting.
result ITDM reduces overfitting and improves DNN training.
Method learns statistics of return distributions via neural networks and maximum mean discrepancy.
problem Learning probability distributions in reinforcement learning.
method Maximum mean discrepancy (MMD) for learning unrestricted statistics of return distributions.
result Method outperforms standard distributional RL baselines on Atari games.
This paper resolves the all-or-nothing phase transition in graph matching.
problem Recovering vertex correspondence between edge-correlated random graphs.
method Analysis of mutual information, truncated second-moment computation, and maximum likelihood estimator.
result Sharp thresholds for correct matching in both dense and sparse graphs.
Submodular functions have many applications. Matchings have many applications. The bitext word alignment problem can be modeled as the problem of maximizing a nonnegative, monotone, submodular function constrained to matchings in a complete bipartite graph where each vertex corresponds to a word in the two input senten…
Dual training method for EBMs with overparametrized neural networks.
problem Training EBMs with non-convex energies is challenging.
method Derive variational principles and dual GDA algorithm for feature-learning regime.
result Dual GDA algorithm performs best with similar time scales for features and particles.
A common challenge in estimating parameters of probability density functions is the intractability of the normalizing constant. While in such cases maximum likelihood estimation may be implemented using numerical integration, the approach becomes computationally intensive. The score matching method of Hyvärinen [2005] …
We improve maximum likelihood for location estimation in finite samples.
problem Estimating a parameter from samples with unknown or varying distribution.
method Use smoothed Fisher information for finite sample size and varying distributions.
result Recover optimal estimation theory for finite n and arbitrary f. Portfolio selection is the central task for assets management, but it turns out to be very challenging. Methods based on pattern matching, particularly the CORN-K algorithm, have achieved promising performance on several stock markets. A key shortage of the existing pattern matching methods, however, is that the risk i…
MGD combines maximum entropy and diffusion methods for efficient sampling.
problem Generating samples from limited information in high dimensions.
method Moment Guided Diffusion (MGD) using stochastic differential equations.
result MGD efficiently samples maximum entropy distributions in finite time.
A new method for training diffusion models using likelihood matching.
problem Training efficient and accurate diffusion models.
method Likelihood Matching approach, quasi-likelihood approximation, score and Hessian estimation.
result Consistent matching of first two transitional moments between diffusion steps.
New research shows the maximum ℓ1-margin classifier doesn't adapt to sparse ground truths.
problem Understanding the limitations of the maximum ℓ1-margin classifier in high-dimensional settings.
method Analyzing convergence and prediction error rates of the maximum ℓ1-margin classifier.
result Proves tight upper and lower bounds for prediction error, showing benign overfitting.
Proves necessity of at least log2(n) layers to compute maximum of n numbers.
problem Computing the maximum of n numbers with ReLU neural networks.
method Uses lattice polytopes and duality with Newton polytopes to prove depth lower bounds.
result Proves that log2(n) hidden layers are necessary and sufficient.
Adding random features to GNNs improves their performance.
problem Limitations of GNNs in distinguishing graphs and learning efficient algorithms.
method Adding random features to each node in GNNs.
result Random features enable GNNs to learn optimal algorithms for graph problems.
CO2 algorithm creates coresets for generic smooth divergences efficiently.
problem Efficiently creating coresets for generic smooth divergences.
method CO2 algorithm using functional Taylor expansion and maximum mean discrepancy minimization.
result Poly-logarithmically many data points suffice for Sinkhorn divergence approximation.
When maximum likelihood estimation is infeasible, one often turns to score matching, contrastive divergence, or minimum probability flow to obtain tractable parameter estimates. We provide a unifying perspective of these techniques as minimum Stein discrepancy estimators, and use this lens to design new diffusion kerne…
Study reconstructs hidden perfect matchings in random graphs with specific edge weights.
problem Reconstructing hidden perfect matchings in random weighted bipartite graphs.
method Analyzes the maximum likelihood estimator for matching reconstruction under different probability distributions of edge weights.
result Sharp threshold and infinite-order phase transition in reconstruction error for different probability distributions.
A group of transition probability functions form a Shannon's channel whereas a group of truth functions form a semantic channel. Label learning is to let semantic channels match Shannon's channels and label selection is to let Shannon's channels match semantic channels. The Channel Matching (CM) algorithm is provided f…
A new layer, funnel, reduces dimensionality in flows for better performance.
problem Training high-dimensional models efficiently and accurately.
method Constructing dimension-reducing surjective flows using the funnel layer.
result The funnel layer improves model performance with a smaller latent space.
Algorithm solves two-sided matching markets with unknown preferences and constraints.
problem Two-sided online matching markets with complementary preferences and quota constraints.
method Formulated as a bandit learning problem, proposed MMTS algorithm combining Thompson Sampling and double matching.
result MMTS achieves stability and linear Bayesian regret with respect to quota and time horizon.