Exact second-order optimization for deep learning reduces computational cost and improves performance.
problem Inadequate use of second-order optimization methods in deep learning due to high computational cost and non-convexity.
method Developed an exact stochastic second-order Newton method that addresses the non-convexity issue and provides an expression for the stochastic Hessian.
result Exact second-order Newton direction formula and its application in deep learning datasets.
Exact learning improves naive Bayes classifier performance for small samples.
problem Improving naive Bayes classifier performance with small sample sizes.
method Proposes an exact learning augmented naive Bayes classifier (ANB) that ensures a class variable with no parents.
result The proposed ANB method outperforms other methods in comparison experiments.
We present new algorithms for learning Bayesian networks from data with missing values using a data augmentation approach. An exact Bayesian network learning algorithm is obtained by recasting the problem into a standard Bayesian network learning problem without missing data. To the best of our knowledge, this is the f…
Unsupervised learning of probabilistic models is a central yet challenging problem in machine learning. Specifically, designing models with tractable learning, sampling, inference and evaluation is crucial in solving this task. We extend the space of such models using real-valued non-volume preserving (real NVP) transf…
A new method for optimal filtration learning in time-series data analysis.
problem Finding an optimal filtration for analyzing topological properties of discrete data.
method Formulated an optimization problem and proposed an algorithm for solving it.
result Derivation of the exact formula of the gradient of the loss function with respect to filtration parameters.
Exact risk and learning rate curves derived for adaptive SGD on high-dimensional problems.
problem Analyzing risk and learning rate dynamics in high-dimensional optimization problems.
method Developed a framework to give exact expressions for risk and learning rate curves using ODEs.
result Exact expressions for risk and learning rate curves, with detailed analysis of two adaptive learning rates.
Determinantal point processes (DPPs) are an important concept in random matrix theory and combinatorics. They have also recently attracted interest in the study of numerical methods for machine learning, as they offer an elegant "missing link" between independent Monte Carlo sampling and deterministic evaluation on reg…
New method learns stochastic process representations without exact reconstruction.
problem Learning exact representations of high-dimensional noisy stochastic processes.
method CReSP framework for contrastive learning of stochastic processes.
result Effective for learning representations of various stochastic processes.
Study exact partition recovery with same-cluster oracle, bounded error.
problem Exact recovery of partitions with same-cluster oracle in adversarial error.
method Novel connection to correlation clustering, Rényi-Ulam framework, upper and lower bounds, randomized algorithm analysis, adaptivity-query complexity study.
result Upper and lower bounds on worst-case query complexity, expected performance bounds of randomized algorithm.
In this paper, we propose exact passive-aggressive (PA) online algorithms for learning to rank. The proposed algorithms can be used even when we have interval labels instead of actual labels for examples. The proposed algorithms solve a convex optimization problem at every trial. We find exact solution to those optimiz…
This work presents novel algorithms for learning Bayesian network structures with bounded treewidth. Both exact and approximate methods are developed. The exact method combines mixed-integer linear programming formulations for structure learning and treewidth computation. The approximate method consists in uniformly sa…
New conditions ensure Dantzig-Wolfe relaxation matches rank-constrained optimization problems.
problem Rank-constrained optimization problems with linear matrix inequalities.
method Investigates Dantzig-Wolfe relaxation and develops conditions for exactness.
result Conditions for extreme point, convex hull, and objective exactness.
FLASH-MAX predicts electromagnetic fields from sparse data in seconds.
problem Predicting homogeneous electromagnetic fields from sparse pointwise observations.
method Exact-by-construction neural network architecture that satisfies Maxwell's equations symbolically.
result FLASH-MAX achieves sub-1% relative validation error from 1K sparse observations in seconds.
Federated learning supports exact support recovery with minimal communication.
problem Learning the exact support of sparse linear regression in federated learning.
method One-shot communication algorithm for exact support recovery without optimization.
result Polynomial sample complexity and logarithmic number of clients required.
We show how to convert ICL in linearized transformers into model weights.
problem Making in-context learning interpretable and permanent in large language models.
method Demonstrates equivalence between ICL and bias terms in linearized transformers, and develops ICLCA for exact conversion.
result Exact conversion of in-context learning into model weights is possible for linearized transformers.
Improved causal discovery methods for large graphs without strict assumptions.
problem Sub-optimal solutions due to faithfulness assumption violations.
method Super-structure estimation and local search strategies.
result The proposed method scales to hundreds of nodes with high accuracy.
Study on ReLU regression with Massart noise, achieving exact parameter recovery.
problem Efficiently fitting ReLUs to data in the presence of Massart noise.
method Developed an efficient algorithm for exact parameter recovery under mild assumptions.
result Achieved exact parameter recovery in ReLU regression with Massart noise.
New kernel enables exact GP analysis of massive datasets.
problem Limited scalability and flexibility of traditional GPs for large data sets.
method Explicitly derived nonstationary kernel for large-scale GP analysis.
result Novel kernel outperforms existing methods in synthetic and real-world applications.
Machine learning boosts RCT efficiency by controlling type I error and improving statistical power.
problem Improving statistical efficiency in RCTs with complex covariate adjustments.
method Machine learning-assisted adjustment under Rosenbaum's framework for exact tests.
result The proposed method robustly controls type I error and significantly boosts statistical efficiency.
Recent findings in multi-agent deep learning systems point towards the emergence of compositional languages. These claims are often made without exact analysis or testing of the language. In this work, we analyze the emergent language resulting from two different cooperative multi-agent game with more exact measures fo…
This is the third part of the work on the exact triangles. We construct chain homomorphisms and show exactness of the resulting sequence.
Exact recovery of tensor decomposition (TD) methods is a desirable property in both unsupervised learning and scientific data analysis. The numerical defects of TD methods, however, limit their practical applications on real-world data. As an alternative, convex tensor decomposition (CTD) was proposed to alleviate thes…
Learning-to-rank techniques have proven to be extremely useful for prioritization problems, where we rank items in order of their estimated probabilities, and dedicate our limited resources to the top-ranked items. This work exposes a serious problem with the state of learning-to-rank algorithms, which is that they are…
This paper analyzes how periodic and soft target updates stabilize linear Q-learning.
problem Theoretical explanation of stabilization mechanisms for linear Q-learning.
method Exact analysis using switched linear system dynamics and the joint spectral radius.
result Periodic and soft target updates can guarantee convergence to the exact projected Q-Bellman solution under specific conditions.
Proposes exact inference for continuous-time Gaussian process dynamics.
problem Inexact inference methods for continuous-time Gaussian process dynamics are impractical for irregularly-sampled data.
method Uses higher-order numerical integrators to discretize dynamics with arbitrary accuracy and proposes multistep and Taylor integrators for exact inference.
result Demonstrates accurate representation of continuous-time systems through exact GP inference.
The paper proposes a method to learn the structure of continuous-action games with non-parametric utilities using a limited number of samples.
problem Learning the exact structure of continuous-action games with non-parametric utility functions.
method An ℓ1 regularized method that encourages sparsity of the Fourier transform coefficients of the utility functions, accessed via a few Nash equilibria and their noisy utilities. result The method recovers the exact structure of the utility functions and the game structure with provable theoretical guarantees.
We prove an exact relationship between the optimal denoising function and the data distribution in the case of additive Gaussian noise, showing that denoising implicitly models the structure of data allowing it to be exploited in the unsupervised learning of representations. This result generalizes a known relationship…
Study on compact manifolds for exact G2-Structures without additional constraints.
problem Whether compact 7-manifolds support exact G2-Structures. method Investigate exact G2-Structures on compact manifolds, considering relationships with other conditions. result Initiate a study on exact G2-Structures on compact manifolds without additional constraints. We develop nested automatic differentiation (AD) algorithms for exact inference and learning in integer latent variable models. Recently, Winner, Sujono, and Sheldon showed how to reduce marginalization in a class of integer latent variable models to evaluating a probability generating function which contains many leve…
In this paper, we provide a unified analysis of temporal difference learning algorithms with linear function approximators by exploiting their connections to Markov jump linear systems (MJLS). We tailor the MJLS theory developed in the control community to characterize the exact behaviors of the first and second order …
Defines band maps in unoriented link Floer homology forming a skein exact triangle.
problem Understanding unoriented link Floer homology through band maps.
method Defines and analyzes band maps in unoriented link Floer homology.
result Band maps form an unoriented skein exact triangle.
Compact learning results across various loss functions.
problem Understanding sample complexity in transductive learning.
method Analyzing finite projections and sample complexities for different loss functions.
result Exact compactness of sample complexity holds broadly across realizable and agnostic learning.
New model for community detection with side information improves recovery accuracy.
problem Community detection in networks with additional node data.
method Data Block Model (DBM) with Chernoff--TV divergence for threshold characterization and efficient algorithm.
result Sharp exact recovery threshold and efficient algorithm for DBM.
Non-exact Poisson structures found on toric varieties.
problem Existence of exact Poisson structures on toric varieties.
method Geometric criterion for non-exactness of Poisson structures with finite symplectic leaves.
result Non-exactness of Poisson structures on projective toric varieties.
Exact selective inference with randomization for Gaussian regression models.
problem Exact selective inference in Gaussian regression models.
method Introduces a pivot for exact selective inference with randomization, reducing the problem to a bivariate truncated Gaussian distribution.
result Our pivot leads to exact inference and produces narrower confidence intervals than related methods.
Compression is at the heart of effective representation learning. However, lossy compression is typically achieved through simple parametric models like Gaussian noise to preserve analytic tractability, and the limitations this imposes on learning are largely unexplored. Further, the Gaussian prior assumptions in model…
Exact discrete mechanics for nonholonomic systems defined.
problem Discrete mechanics for nonholonomic systems.
method Constructing an exponential map and deriving exact discrete nonholonomic integrators.
result Reproduces continuous nonholonomic flow as discrete flow on constraint submanifold.
ShuffleNet is a state-of-the-art light weight convolutional neural network architecture. Its basic operations include group, channel-wise convolution and channel shuffling. However, channel shuffling is manually designed empirically. Mathematically, shuffling is a multiplication by a permutation matrix. In this paper, …
Exact learning of tree-structured models with side info and noise.
problem Learning tree-structured graphical models with side information and noise.
method Probabilistic tools from strong large deviations theory.
result Exact asymptotics of structure learning from samples.
Open problem: Establishing bounds for Cayley-table completion to discover discrete algorithmic axioms.
problem Discovering discrete algorithmic axioms missing in deep learning.
method Cayley-table completion as a testbed for algorithmic complexity minimization.
result Formal exact recovery bounds for Cayley-table completion.
For a Legendrian (2,n) torus knot or link with maximal Thurston-Bennequin number, Ekholm, Honda, and Kálmán constructed Cn exact Lagrangian fillings, where Cn is the n-th Catalan number. We show that these exact Lagrangian fillings are pairwise non-isotopic through exact Lagrangian isotopy. To do that, we com…
Decentralized Gaussian processes for multi-agent systems.
problem Scalable and flexible learning solutions for multi-agent systems.
method Asymptotically exact decentralized solution to Gaussian processes, with online Bayesian model averaging for hyperparameter selection.
result Asymptotically exact decentralized Gaussian process approximation and online Bayesian model averaging.
EGN optimizes deep neural networks with exact Gauss-Newton for large-scale problems.
problem Training deep neural networks efficiently and accurately.
method Stochastic second-order optimization using low-rank linear algebra and matrix factorization.
result Converges to stationary points of the objective function under mild assumptions.
Exact inference method for Wasserstein distance with finite-sample coverage.
problem Asymptotic approximation methods for Wasserstein distance lack finite-sample validity.
method Selective Inference inspired approach for exact inference.
result Valid confidence interval for Wasserstein distance with finite-sample coverage.
In many machine learning applications, crowdsourcing has become the primary means for label collection. In this paper, we study the optimal error rate for aggregating labels provided by a set of non-expert workers. Under the classic Dawid-Skene model, we establish matching upper and lower bounds with an exact exponent …
Efficient algorithm for matching graphs with community structure.
problem Graph matching between correlated stochastic block models with constant correlation.
method Partition trees rooted from each vertex, comparing edge statistics to different communities.
result First low-order polynomial-time algorithm achieving exact matching with high probability in dense graphs.
Wasserstein distance plays increasingly important roles in machine learning, stochastic programming and image processing. Major efforts have been under way to address its high computational complexity, some leading to approximate or regularized variations such as Sinkhorn distance. However, as we will demonstrate, regu…
Double descent refers to the phase transition that is exhibited by the generalization error of unregularized learning models when varying the ratio between the number of parameters and the number of training samples. The recent success of highly over-parameterized machine learning models such as deep neural networks ha…