NT probability measures knotting in 3D arc systems.
problem Measuring knotting in 3D arc systems.
method Transforming polygonal arcs into unique diagrams, generalizing NT probability.
result Properties of NT probability for 3D arc systems are shown.
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48 results for “NT probability”
Non-trivialization probability of arc system in 3D space
problem Defining and generalizing the knotting probability of an arc diagram in 3D space
method Transforming polygonal arcs in 3D space into unique arc diagrams
result Introducing and generalizing the Non-Trivialization probability (NT probability) for arc systems in 3D space
Survey on negative transfer in machine learning.
problem Negative transfer in transfer learning reduces target domain performance.
method Systematic review of 50+ approaches to mitigate negative transfer.
result Lack of systematic survey on negative transfer.
A Dynamic Chain Event Graph (DCEG) provides a rich tree-based framework for modelling a dynamic process with highly asymmetric developments. An N Time-Slice DCEG (NT-DCEG) is a useful subclass of the DCEG class that exhibits a specific type of periodicity in its supporting tree graph and embodies a time-homogeneity ass…
NTS-NOTEARS learns DBNs from time-series data with prior knowledge.
problem Learning dynamic Bayesian networks from time-series data with nonlinear and lagged relationships.
method Uses 1D CNNs to model DBNs, incorporating prior knowledge as constraints.
result Achieves state-of-the-art DAG structure quality compared to parametric and nonparametric methods.
The Dynamic Chain Event Graph (DCEG) is able to depict many classes of discrete random processes exhibiting asymmetries in their developments and context-specific conditional probabilities structures. However, paradoxically, this very generality has so far frustrated its wide application. So in this paper we develop an…
This paper presents a novel clustering concept that is based on jointly learned nonlinear transforms (NTs) with priors on the information loss and the discrimination. We introduce a clustering principle that is based on evaluation of a parametric min-max measure for the discriminative prior. The decomposition of the pr…
Uniform bounds for neural networks' generalization error in overparameterized settings.
problem Generalization error in overparameterized neural networks.
method Neural Tangent kernel theory and Mercer decomposition of the NT kernel in spherical harmonics.
result Uniform generalization bounds for overparameterized neural networks in RKHS.
Having a sequence-to-sequence model which can operate in an online fashion is important for streaming applications such as Voice Search. Neural transducer is a streaming sequence-to-sequence model, but has shown a significant degradation in performance compared to non-streaming models such as Listen, Attend and Spell (…
New algorithms achieve optimal regret in sliding window model with limited memory.
problem Experts problem in the sliding window model with limited information.
method 2 queries, polylog(nT) memory, exponential improvement on memory.
result Achieve optimal regret of sqrt(nW)polylog(nT) with 2 queries and polylog(nT) memory.
Fast Estimation of Information Theoretic Learning Descriptors using Explicit Inner Product Spacescs.LG
Kernel methods form a theoretically-grounded, powerful and versatile framework to solve nonlinear problems in signal processing and machine learning. The standard approach relies on the \emph{kernel trick} to perform pairwise evaluations of a kernel function, leading to scalability issues for large datasets due to its …
Neural networks can interpolate random data but still generalize well, studied in the NT regime.
problem Understanding how neural networks interpolate random labels and generalize well in the overparametrized regime.
method Characterization of the eigenstructure of the empirical NT kernel and generalization error of NT ridge regression.
result The generalization error is well approximated by polynomial ridge regression with an increased regularization parameter.
New analysis of signSGD with random reshuffling shows faster convergence rates.
problem Understanding the convergence of signSGD with random reshuffling in nonconvex optimization.
method Developed new sign-based algorithms (SignRVR, SignRVM) and analyzed convergence rates.
result Achieved faster convergence rates for signSGD with random reshuffling.
Paper discusses new stochastic algorithms for sparse signal recovery.
problem Sparse signal recovery in medical imaging and remote sensing.
method Proposes and analyzes stochastic natural thresholding algorithms.
result Demonstrates improved performance of StoNT algorithms.
New algorithms reduce private bandit regret to nearly non-private levels.
problem Differentially private adversarial bandits and expert advice.
method Conversion of non-private algorithms to private, new algorithms for bandits and expert advice.
result Improved regret bounds for private bandits, sublinear for small ε.
This paper examines the impact of random initialization in neural networks using NTK theory.
problem Understanding the impact of random initialization in neural networks using NTK theory.
method Analyzes the convergence of training dynamics and generalization error of wide neural networks with random initialization.
result The generalization error of wide neural networks trained by gradient descent is \( \Omega(n^{-\frac{3}{d+3}}) \), highlighting the benefits of mirror initialization and suggesting limitations of NTK theory.
Optimizes profit in targeted marketing across multiple markets with varying marketing expenditures.
problem Maximizing profit in a sequential marketing strategy with multiple markets and varying marketing costs.
method Near-optimal algorithms in an adversarial bandit setting, proving regret bounds for different demand curve types.
result Proved near-optimal regret bounds for the profit-maximization problem in targeted marketing.
Unified toolkit for comparing neural representations using SRTD and NTS.
problem Heuristic asymmetry and unbounded scores in existing divergences.
method Developed SRTD and NTS to address these issues.
result Unified, robust, and scale-invariant metric for comparing neural representations.
In this paper, we study the algebraic properties of the higher analogues of Courant algebroid structures on the direct sum bundle for an -dimensional manifold. As an application, we revisit Nambu-Poisson structures and multisymplectic structures. We prove that the graph of an -vector fi…
Proportional transaction costs present difficult theoretical problems in trading algorithm design, on account of their lack of analytical tractability. The author derives a solution of DT-NT-DT form for an arbitrary model in which the the traded asset has diffusive dynamics described by one or more stochastic risk fact…
In this paper, we show that the spaces of sections of the -th differential operator bundle $\dev^n E$ and the -th skew-symmetric jet bundle $\jet_n E$ of a vector bundle are isomorphic to the spaces of linear -vector fields and linear -forms on respectively. Consequently, the -omni-Lie algebroi…
We consider assets for which price and squared volatility are jointly driven by Heston joint stochastic differential equations (SDEs). When the parameters of these SDEs are estimated from sub-sampled data , estimation errors do impact the classical option pricing PDEs. We estimate thes…
SPARQ-SGD: Event-Triggered and Compressed Communication in Decentralized Stochastic Optimizationstat.ML
In this paper, we propose and analyze SPARQ-SGD, which is an event-triggered and compressed algorithm for decentralized training of large-scale machine learning models. Each node can locally compute a condition (event) which triggers a communication where quantized and sparsified local model parameters are sent. In SPA…
Knots parametrized in cylinder coordinates by t -> (st, 3 + cos(nt), cos(mt + φ)) share properties of Lissajous and billiard knots in a cylinder. We use these 'billiard knots in a flat solid torus' to study two topics: when is Z(s,n,m) equal to Z(s,m,n)? And: why are the determinants of certain Lissajous and billiard k…
We propose maximum likelihood estimation for learning Gaussian graphical models with a Gaussian (ell_2^2) prior on the parameters. This is in contrast to the commonly used Laplace (ell_1) prior for encouraging sparseness. We show that our optimization problem leads to a Riccati matrix equation, which has a closed form …
We study the supervised learning problem under either of the following two models: (1) Feature vectors are -dimensional Gaussians and responses are for an unknown quadratic function; (2) Feature vectors are distributed as a mixture of two $…
In this paper, we propose the first computationally efficient projection-free algorithm for bandit convex optimization (BCO). We show that our algorithm achieves a sublinear regret of (where is the horizon and is the dimension) for any bounded convex functions with uniformly bounded gradients. We …
New analysis shows Local SGD can achieve error scaling with only fixed number of communications.
problem Speeding up SGD by parallelizing across multiple workers with reduced communication overhead.
method Proposed and analyzed Local SGD method with a fixed number of communications independent of the number of steps.
result Achieves an error scaling as 1/(nT) with only a fixed number of communications (Ω(n)).
While training a machine learning model using multiple workers, each of which collects data from their own data sources, it would be most useful when the data collected from different workers can be {\em unique} and {\em different}. Ironically, recent analysis of decentralized parallel stochastic gradient descent (D-PS…
We consider decentralized stochastic optimization with the objective function (e.g. data samples for machine learning task) being distributed over machines that can only communicate to their neighbors on a fixed communication graph. To reduce the communication bottleneck, the nodes compress (e.g. quantize or sparsi…
HD algorithm simulates dynamics on random matrix ensembles without generating full matrices.
problem Simulating dynamics on dense random matrix ensembles with high space and time complexity.
method Householder reflectors for adaptive and recursive construction, deferring decisions.
result Significant reductions in runtime and memory footprint for practical .
Empirical study compares wide neural networks to kernel methods, resolving open questions.
problem Understanding the relationship between wide neural networks and kernel methods.
method Large-scale empirical study using various neural network architectures and kernel methods.
result Wide neural networks outperform fully-connected finite-width networks in some cases, but underperform convolutional finite-width networks.
We continue the study of the spectral theory associated to integrable metrics, started in our previous paper arXiv:1301.1793 [math.SP]. We introduce the notion of 1-integrable metric on line-bundles on a compact Riemann surface. We extend the spectral theory of generalized Laplacians to line-bundles equipped with 1-int…
In the present paper, we study globally framed f-manifolds in the particular setting of indefinite S-manifolds for both spacelike and timelike cases. We prove that if is a warped CR-submanifold such that is ?-anti-invariant and NT is ?-invariant, then M is a CR-product. We…
The goal of this paper is to offer a comprehensive exposition of the current knowledge about Heegaard splittings of exteriors of knots in the 3-sphere. The exposition is done with a historical perspective as to how ideas developed and by whom. Several new notions are introduced and some facts about them are proved. In …
New optimal rates for score estimation improve diffusion model performance.
problem Improving statistical rates for score estimation in diffusion models.
method Sharp minimax rates for score estimation of diffused distributions.
result Achieves sharp minimax rate without extraneous logarithmic terms.
A decentralized algorithm minimizes cumulative regret in stochastic linear bandits with safety constraints.
problem Efficiently solving a linear bandit-optimization problem over a network of agents with safety constraints.
method DLUCB: a fully decentralized algorithm that minimizes cumulative regret through UCB strategy and consensus procedure.
result Near-optimal regret performance of with communication rate.
The systole length of hyperbolic n-manifolds is bounded by a function of n and t.
problem Bounding the systole length of hyperbolic n-manifolds.
method Relating the number of simplices to the diameter, and using bounds on Margulis tubes.
result The systole length is bounded by a function of n and t.
New method improves convergence of SPP for convex optimization problems.
problem Stochastic optimization and robustness to SGD.
method Minibatch Stochastic Proximal Point (M-SPP) method with stability analysis.
result M-SPP achieves faster convergence rates under smoothness and quadratic growth conditions.
Agents collaborate to minimize regret while keeping costs under a threshold.
problem Collaborative multi-agent stochastic linear bandits with cost constraints.
method Safe distributed upper confidence bound algorithm (MA-OPLB) with accelerated consensus.
result Regret bound of order $ \mathcal{O}\left(\frac{d}{τ-c_0}\frac{\log(NT)^2}{\sqrt{N}}\sqrt{\frac{T}{\log(1/|λ_2|)}}
ight)$.
Forward-looking portfolio selection with multivariate non-Gaussian models and the Esscher transformq-fin.PM
In this study we suggest a portfolio selection framework based on option-implied information and multivariate non-Gaussian models. The proposed models incorporate skewness, kurtosis and more complex dependence structures among stocks log-returns than the simple correlation matrix. The two models considered are a multiv…
Decentralized training of deep learning models is a key element for enabling data privacy and on-device learning over networks, as well as for efficient scaling to large compute clusters. As current approaches suffer from limited bandwidth of the network, we propose the use of communication compression in the decentral…
Thompson Sampling is one of the oldest heuristics for multi-armed bandit problems. It is a randomized algorithm based on Bayesian ideas, and has recently generated significant interest after several studies demonstrated it to have better empirical performance compared to the state of the art methods. In this paper, we …
Study MNL-Bandit in non-stationary settings with optimal regret bound.
problem Optimizing decisions in a non-stationary environment for multi-armed bandit problems.
method Develops an algorithm with worst-case expected regret bound and introduces new techniques to handle non-stationarity.
result Optimal regret bound proven for the MNL-Bandit problem in non-stationary environments.
Thompson Sampling remains differentially private with minimal modifications.
problem Ensuring privacy in Thompson Sampling for multi-arm bandits.
method Demonstrated differential privacy of original Thompson Sampling, provided per-round guarantees, and introduced modifications for tighter privacy.
result Privacy guarantees can be tuned by modifying the algorithm, and these modifications impact expected regret.
Text-based analysis methods allow to reveal privacy relevant author attributes such as gender, age and identify of the text's author. Such methods can compromise the privacy of an anonymous author even when the author tries to remove privacy sensitive content. In this paper, we propose an automatic method, called Adver…
We analyze the convergence of gradient-based optimization algorithms that base their updates on delayed stochastic gradient information. The main application of our results is to the development of gradient-based distributed optimization algorithms where a master node performs parameter updates while worker nodes compu…
A new online learning setting for autoregressive processes with sublinear regret.
problem Sequential decision-making with temporal dependence in autoregressive processes.
method Autoregressive Bandits (ARBs) and AutoRegressive Upper Confidence Bound (AR-UCB) algorithm.
result Sublinear regret of order $\widetilde{\mathcal{O}} \left( \frac{(k+1)^{3/2}\sqrt{nT}}{(1-Γ)^2}
ight)$ for optimal policy.