Study shows challenges in reinforcement learning math problems, proposing enhancements and a hardness measure.
problem Challenges in reinforcement learning finding rare high-reward instances.
method Combining combinatorial group theory, algorithmic enhancements, and topological hardness measure.
result Resolved mathematical questions and proposed enhancements for reinforcement learning.
Corrects technical error in change of measure for HTB models.
problem Technical error in change of measure for HTB models.
method Provided supplement conditions to correct the error.
result Corrected technical error in change of measure for HTB models.
Paper analyzes BIHT for noisy 1-bit CS, improving results with up to τ-fraction of incorrect measurements.
problem Estimating sparse vectors from noisy sign measurements in 1-bit compressed sensing.
method Binary Iterative Hard Thresholding (BIHT) algorithm, using Gaussian matrices and high-dimensional geometry analysis.
result BIHT provides estimates within ε+τ error with τ-fraction of incorrect measurements, maintaining universality of measurements.
AVH scores measure sample hardness, improving model calibration.
problem CNNs' poor calibration and overconfidence issues.
method AVH score based on normalized angular distance between feature embeddings and target classifiers.
result AVH scores correlate with human visual hardness and improve model calibration.
Estimating IPM is as hard as estimating under IPM, both requiring similar optimal rates.
problem Estimating Integral Probability Metrics (IPMs) between probability measures.
method Study of minimax optimal rates for IPM estimation and under IPM estimation based on samples.
result Minimax optimal rates for estimating IPM and estimating under IPM are multiplicatively equivalent.
Study shows exponential sample complexity for stabilizing certain linear systems.
problem Statistical hardness of learning to stabilize linear time-invariant systems.
method Analysis of sample complexity and co-stabilizability using robust control ideas.
result Sample complexity increases exponentially with system dimension.
Proves hardness of semi-discrete optimal transport and proposes regularization methods.
problem Computing Wasserstein distance between discrete and non-discrete probability measures.
method Proves hardness, introduces distributionally robust dual optimal transport, regularizes primal objective, uses stochastic gradient descent.
result Regularization schemes and improved convergence guarantees for semi-discrete optimal transport problems.
Financial markets are not random, but hard to predict due to hidden causes and strategic use.
problem Hard to predict financial markets
method Disciplined thesis on the distinction between no-arbitrage, informational efficiency, and net exploitability
result Discovers that markets are hard to predict due to hidden causes and strategic use
IHT improves sparse distribution learning.
problem Learning sparse discrete distributions.
method Iterative hard thresholding as a solution, with a greedy approximate projection.
result IHT achieves state of the art results for sparse distribution learning.
Binary Iterative Hard Thresholding converges with optimal number of 1-bit measurements.
problem Recovering sparse signals from 1-bit compressed measurements.
method Binary Iterative Hard Thresholding (BIHT) algorithm.
result BIHT converges with only O(k/ε) measurements, optimal for recovery.
Meta-learning strategy improves few-shot classification performance.
problem Few-shot classification with deep neural networks struggles when labeled samples are limited.
method Proposes an easy-to-hard expert meta-training strategy to arrange training tasks based on task hardness.
result Meta-learners achieve better results with the proposed expert training strategy.
New RF dissimilarity measures improve multi-view learning accuracy.
problem Improving multi-view learning accuracy in HDLSS problems.
method Modified Random Forest proximity measures for HDLSS multi-view classification.
result Second method significantly more accurate than other state-of-the-art methods.
New findings on maximizing noise stability in partitions of Gaussian space.
problem Maximizing noise stability in partitions of Gaussian space.
method Analyzing the correlation between sets and their noise stability, proving conditional conjectures and hardness results.
result Hyperstable partitions maximize noise stability and have specific properties.
An algorithmically hard phase was described in a range of inference problems: even if the signal can be reconstructed with a small error from an information theoretic point of view, known algorithms fail unless the noise-to-signal ratio is sufficiently small. This hard phase is typically understood as a metastable bran…
Paper tackles 1-bit compressed sensing, presenting efficient algorithm for sparse signal estimation.
problem Estimating sparse signals from binary measurements.
method Non-convex sparsity-constrained program with one-shot hard thresholding.
result Simple algorithm produces accurate signal approximation with high probability.
Sparse linear regression is hard to solve efficiently, even with k-sparse solutions.
problem Sparse linear regression problem with k-sparse solutions.
method Fine-grained complexity and hardness assumptions.
result No better-than-brute-force algorithms exist for sparse linear regression.
This paper explains the math behind a generative adversarial network (GAN) model and why it is hard to be trained. Wasserstein GAN is intended to improve GANs' training by adopting a smooth metric for measuring the distance between two probability distributions.
Coresets are efficient representations of data sets such that models trained on the coreset are provably competitive with models trained on the original data set. As such, they have been successfully used to scale up clustering models such as K-Means and Gaussian mixture models to massive data sets. However, until now,…
We consider stochastic gradient descent (SGD) for least-squares regression with potentially several passes over the data. While several passes have been widely reported to perform practically better in terms of predictive performance on unseen data, the existing theoretical analysis of SGD suggests that a single pass i…
Proposes new random models for fuzzy clustering similarity measures.
problem Challenges in choosing a random model for fuzzy clustering similarity measures.
method Introduces three intuitive and explainable random models for fuzzy clusterings.
result Each random model has distinct behavior, emphasizing the importance of accurate model selection.
Graph neural networks struggle to distinguish certain graph structures.
problem Difficulty in distinguishing graphs with graph neural networks.
method Analysis of communication capacity in message-passing model of graph neural networks.
result Capacity of MPNN needs to grow linearly for trees and quadratically for general connected graphs.
New lower bounds show sparse recovery is hard even with multiple preconditioners.
problem Sparse recovery with ill-conditioned designs is hard for certain algorithms.
method Constructing a single signal distribution that multiple preconditioned Lasso programs fail on.
result Standard sparse random designs are robust to erasures, aiding sparse recovery.
Recovery of low-rank matrices from a small number of linear measurements is now well-known to be possible under various model assumptions on the measurements. Such results demonstrate robustness and are backed with provable theoretical guarantees. However, extensions to tensor recovery have only recently began to be st…
New algorithms optimize a soft-robust criterion in reinforcement learning, reducing conservatism.
problem Computing robust policies for high-stakes decisions with limited data.
method Soft-robust criterion using risk measures, two algorithms for optimization.
result Our algorithms produce less conservative solutions than existing methods.
Study on computing and estimating calibration distance, showing hardness and efficiency.
problem Computing and estimating calibration distance under different assumptions.
method Efficient algorithm for exact computation, polynomial-time approximation scheme; sample-based estimation for upper bounds.
result The problem becomes NP-hard when assumptions are removed, but efficient algorithms exist under certain conditions.
Trivial links are unique up to number of link components, but they can be hard to recognize from arbitrary diagrams. We define a new measure of the complexity of a link embedding, the crumple, and show how this may be used to measure progress toward a trivial embedding. In conjunction with a modified form of arc presen…
Developed a new thresholding method that connects soft and hard thresholding.
problem Connecting soft and hard thresholding methods in data analysis.
method Scaled soft thresholding method with empirical scaling values.
result Found two sources of over-fitting in the scaled soft thresholding method.
New algorithm resists contamination in high-dimensional regression with optimal performance.
problem Adversarial and measurement errors in high-dimensional data.
method Adversarial Contamination-resistant Iterative Hard Thresholding (AC-IHT) algorithm.
result Achieves minimax near-optimal estimation and signal-adaptive support recovery.
We introduce a new family of minmax rank aggregation problems under two distance measures, the Kendall τ and the Spearman footrule. As the problems are NP-hard, we proceed to describe a number of constant-approximation algorithms for solving them. We conclude with illustrative applications of the aggregation methods on…
Study uncovers bias in image classification models using attribution maps.
problem Data bias in image classification models.
method Created an artificial dataset with known bias, trained CNNs, and used attribution maps to inspect decisions.
result Different attribution map techniques highlight bias better than others, and metrics support bias identification.
Hard to approximate critical points for simple nonconvex functions.
problem Approximating critical points of nonconvex functions.
method Proving hardness results for polynomial-time approximation of critical points.
result Proving that approximating critical points is intractable for simple nonconvex functions.
New method improves structure learning on sparse graphs.
problem Structure learning on sparse directed acyclic graphs (DAGs).
method Bregman proximal gradient method to address non-convex, high-curvature problem.
result Significantly improved convergence and efficiency.
Random forest is widely exploited as an ensemble learning method. In many practical applications, however, there is still a significant challenge to learn from imbalanced data. To alleviate this limitation, we propose a deep dynamic boosted forest (DDBF), a novel ensemble algorithm that incorporates the notion of hard …
This paper is concerned with the hard thresholding operator which sets all but the k largest absolute elements of a vector to zero. We establish a {\em tight} bound to quantitatively characterize the deviation of the thresholded solution from a given signal. Our theoretical result is universal in the sense that it ho…
In this paper, we consider the problem of compressed sensing where the goal is to recover almost all the sparse vectors using a small number of fixed linear measurements. For this problem, we propose a novel partial hard-thresholding operator that leads to a general family of iterative algorithms. While one extreme of …
We study probability measures induced by set functions with constraints. Such measures arise in a variety of real-world settings, where prior knowledge, resource limitations, or other pragmatic considerations impose constraints. We consider the task of rapidly sampling from such constrained measures, and develop fast M…
The paper optimizes stock portfolios with constraints based on performance attribution.
problem Optimizing stock portfolios with performance attribution constraints.
method Minimizes expected tail loss, constrains asset allocation and selection effect, tests on Dow Jones stocks.
result Imposing constraints on asset allocation and selection effect improves portfolio performance.
Paper proves hardness of learning various complex models under local pseudorandom generators.
problem Hardness of learning various complex models.
method Existence of local pseudorandom generators.
result Proves hardness of learning shallow ReLU neural networks and other models.
Paper solves NP-hard sparse mixed linear regression problem with provable guarantees.
problem Sparse mixed linear regression on unlabeled data.
method Invex relaxation for intractable problem with theoretical guarantees.
result Exact recovery of data labels and close approximation of regression parameters.
This work connects hardness of approximation and learning.
problem Hardness of approximation and learnability in machine learning.
method Shows a single hardness property implying both approximation and learning hardness.
result Obtains new results on hardness of approximation and learnability of specific functions.
Study on hard Legendrian unknots using normal rulings.
problem Understanding the complexity of Legendrian unknots in knot theory.
method Using normal rulings to obstruct and construct hard unknot diagrams.
result Construction of infinitely many smoothly hard max-tb unknot diagrams with bounds on minimum possible writhe.
Moving between 3-manifold triangulations is NP-hard
problem Moving between two triangulations of a 3-manifold
method Showing that the number of bistellar moves and sparse degree-two edge collapses is NP-hard
result First NP-hardness result concerning moves between two triangulations of a 3-manifold
Reliable measures of statistical dependence could be useful tools for learning independent features and performing tasks like source separation using Independent Component Analysis (ICA). Unfortunately, many of such measures, like the mutual information, are hard to estimate and optimize directly. We propose to learn i…
Deciding effective and timely preventive measures against complex social problems affecting relatively low income geographies is a difficult challenge. There is a strong need to adopt intelligent automation based solutions with low cost imprints to tackle these problems at larger scales. Starting with the hypothesis th…
Hard instances, which require a long time for a specific algorithm to solve, help (1) analyze the algorithm for accelerating it and (2) build a good benchmark for evaluating the performance of algorithms. There exist several efforts for automatic generation of hard instances. For example, evolutionary algorithms have b…
We develop mask iterative hard thresholding algorithms (mask IHT and mask DORE) for sparse image reconstruction of objects with known contour. The measurements follow a noisy underdetermined linear model common in the compressive sampling literature. Assuming that the contour of the object that we wish to reconstruct i…
Tackles the computational hardness of HPC detection, conjecturing equivalence to PC detection.
problem Computational hardness of hypergraphic planted clique detection.
method No specific method mentioned; focuses on conjecturing equivalence.
result Equivalence of computational hardness between HPC and PC detection.
Paper tackles optimal network compression for financial systems.
problem Optimal network compression for financial systems under shocks.
method Formulated as an NP-hard problem, studied systemic risk measures, and analyzed specific networks.
result Systemic fragility results no longer hold generally under shocks and heterogeneous networks.