Partial convexification improves tractability of low-rank spectral optimization problems.
problem Minimizing linear objectives subject to matrix inequalities and low-rank constraints.
method Partial convexification of the domain set, deriving rank bounds, and developing a column generation algorithm.
result The partial convexification LSOP-R is equivalent to the original LSOP under certain conditions and yields high-quality solutions.
The paper extends a neural model to estimate uncertainty in multi-interaction trajectory reconstruction.
problem Lack of uncertainty estimation in neural models for multi-interaction trajectory reconstruction.
method Extended Factorised Neural Relational Inference model to output mean and standard deviation for each component of the phase space vector, using various loss functions.
result Demonstrated the importance of physical meaning of variables and existence of local minima during training.
New dual approach for hedging Bermudan options efficiently.
problem Computing efficient hedging portfolios for Bermudan options.
method Pure dual approach, rewriting dual pricing formula as excess reward representation, strict convexification, Monte Carlo method.
result Convergence and effectiveness of the new algorithm tested on various Bermudan options.
The paper tackles fairness in forecasting and learning linear dynamical systems.
problem Under-representation bias in training data for multiple subgroups.
method Introducing subgroup-fair and instant-fair learning of LDS from multiple trajectories of varying lengths, using hierarchies of convexifications of non-commutative polynomial optimisation problems.
result Empirical results show both the beneficial impact of fairness considerations on statistical performance and encouraging effects of exploiting sparsity on run time.
Signal estimation problems with smoothness and sparsity priors can be naturally modeled as quadratic optimization with ℓ0-"norm" constraints. Since such problems are non-convex and hard-to-solve, the standard approach is, instead, to tackle their convex surrogates based on ℓ1-norm relaxations. In this paper…
New algorithm improves dataset distillation with 108% improvement on ImageNet.
problem Improving dataset distillation performance.
method Reparameterization and convexification of implicit gradients (RCIG).
result Establishes new state-of-the-art on various dataset distillation tasks.
Proposes a method to solve deep neural networks' local minimum problem.
problem Local minimum problem in deep neural networks training.
method Transforms cross-entropy loss into risk-averse error criterion, adjusts RSI, and uses convexity region.
result Trained deep learning machine is expected to be inside a global minimum's attraction basin.
New transforms improve signal classification and data analysis.
problem Improving signal classification and data analysis.
method Algebraic generative models and transport transforms.
result Classes of signals are transformed into convex sets, simplifying classification.
Traditionally, most complex intelligence architectures are extremely non-convex, which could not be well performed by convex optimization. However, this paper decomposes complex structures into three types of nodes: operators, algorithms and functions. Iteratively, propagating from node to node along edge, we prove tha…
We introduce normalized nonnegative models (NNM) for explorative data analysis. NNMs are partial convexifications of models from probability theory. We demonstrate their value at the example of item recommendation. We show that NNM-based recommender systems satisfy three criteria that all recommender systems should ide…
Regularized empirical risk minimization with constrained labels (in contrast to fixed labels) is a remarkably general abstraction of learning. For common loss and regularization functions, this optimization problem assumes the form of a mixed integer program (MIP) whose objective function is non-convex. In this form, t…
The omnipresence of deep learning architectures such as deep convolutional neural networks (CNN)s is fueled by the synergistic combination of ever-increasing labeled datasets and specialized hardware. Despite the indisputable success, the reliance on huge amounts of labeled data and specialized hardware can be a limiti…
BP fails to find sparsest solution for structured matrices.
problem Finding sparsest solution to linear equations with structured matrices.
method Introduced class of structured matrices for BP failure.
result Determines columns corresponding to unrecoverable non-zero entries.
Given a C1 planes distribution PT on all Rm we consider {\em horizontal α-harmonic maps}, α≥1/2, with respect to such a distribution. These are maps u∈Hα(Rk,Rm) satisfying PT∇u=∇u and PT(u)(−Δ)αu=0 in D′(Rk). If the distrib…
DCCNNs reduce computational overhead and ambiguity in convolutional neural networks.
problem Reducing computational overhead and ambiguity in convolutional neural networks.
method Introducing a primal learning problem and constructing a dual convex training program, using Fenchel conjugates and Karush-Kuhn-Tucker conditions.
result Eliminates ambiguity and reduces computational overhead in constructing a large kernel matrix.
Sparse regression models are increasingly prevalent due to their ease of interpretability and superior out-of-sample performance. However, the exact model of sparse regression with an ℓ0 constraint restricting the support of the estimators is a challenging (\NP-hard) non-convex optimization problem. In this paper…
New bounds show complexity of adversarial decision making.
problem Understanding sample efficiency in adversarial decision making.
method New upper and lower bounds on Decision-Estimation Coefficient.
result Decision-Estimation Coefficient is necessary and sufficient for low regret in adversarial decision making.
The aim of this paper is to develop a general framework for training neural networks (NNs) in a distributed environment, where training data is partitioned over a set of agents that communicate with each other through a sparse, possibly time-varying, connectivity pattern. In such distributed scenario, the training prob…