arXiv research

AI models help solve a symplectic topology problem.

We elaborate on an idea of M. Abouzaid of equipping the Morse cochain complex of a smooth Morse function on a closed oriented manifold with the structure of an $A_\infty$-algebra. This is a variation on K. Fukaya's definition of Morse-$A_\infty$-categories for closed oriented manifolds involving families of Morse funct…

Motivated by concerns that machine learning algorithms may introduce significant bias in classification models, developing fair classifiers has become an important problem in machine learning research. One important paradigm towards this has been providing algorithms for adversarially learning fair classifiers (Zhang e…

In this paper, we consider derivative free optimization problems, where the objective function is smooth but is computed with some amount of noise, the function evaluations are expensive and no derivative information is available. We are motivated by policy optimization problems in reinforcement learning that have rece…

ES and FD gradients converge as optimization dimension grows.

We address the online linear optimization problem when the actions of the forecaster are represented by binary vectors. Our goal is to understand the magnitude of the minimax regret for the worst possible set of actions. We study the problem under three different assumptions for the feedback: full information, and the …

We propose a novel algorithm for sequential matrix completion in a recommender system setting, where the $(i,j)$th entry of the matrix corresponds to a user $i$'s rating of product $j$. The objective of the algorithm is to provide a sequential policy for user-product pair recommendation which will yield the highest pos…

In this small note we use results derived in Berestycki et al. to correct the celebrated formulae of Hagan et al. We derive explicitly the correct zero order term in the expansion of the implied volatility in time to maturity. The new term is consistent as $β\to 1$. Furthermore, numerical simulations show that it reduc…

We present an off-policy actor-critic algorithm for Reinforcement Learning (RL) that combines ideas from gradient-free optimization via stochastic search with learned action-value function. The result is a simple procedure consisting of three steps: i) policy evaluation by estimating a parametric action-value function;…

As regulators pay more attentions to losses rather than gains, we are able to derive a new class of risk statistics, named regulator-based risk statistics with scenario analysis in this paper. This new class of risk statistics can be considered as a kind of risk extension of risk statistics introduced by Kou et al. \ci…

R package huge simplifies graph estimation for high-dimensional data.

We show that the auxiliary variable method (Møller et al., 2006; Murray et al., 2006) for inference of Markov random fields can be viewed as an approximate Bayesian computation method for likelihood estimation.

Study shows offline RL under $Q^\star$-approximation and partial coverage is harder than previously thought.

Hard to estimate $L^2$-accurate scores without strong assumptions.

Bayesian inference for models that have an intractable partition function is known as a doubly intractable problem, where standard Monte Carlo methods are not applicable. The past decade has seen the development of auxiliary variable Monte Carlo techniques (Møller et al., 2006; Murray et al., 2006) for tackling this pr…

Recent work by Jacot et al. (2018) has shown that training a neural network using gradient descent in parameter space is related to kernel gradient descent in function space with respect to the Neural Tangent Kernel (NTK). Lee et al. (2019) built on this result by establishing that the output of a neural network traine…

DAIS improves AIS by resampling, avoiding gradient issues.

Elastic weight consolidation (EWC, Kirkpatrick et al, 2017) is a novel algorithm designed to safeguard against catastrophic forgetting in neural networks. EWC can be seen as an approximation to Laplace propagation (Eskin et al, 2004), and this view is consistent with the motivation given by Kirkpatrick et al (2017). In…

This paper corrects errors in UMAP's derivation and explains its properties.

Despite remarkable successes, Deep Reinforcement Learning (DRL) is not robust to hyperparameterization, implementation details, or small environment changes (Henderson et al. 2017, Zhang et al. 2018). Overcoming such sensitivity is key to making DRL applicable to real world problems. In this paper, we identify sensitiv…

Research aims to ensure fair classification across explicit and implicit sensitive features.

We identify 'critical windows' in diffusion models where specific features emerge, providing a theoretical framework.

New estimator stabilizes higher-order influence functions for stable statistical inference.

Mirror Langevin Algorithm converges with zero bias.

Stable ResNet stabilizes gradients in deep networks.

New estimator stabilizes higher-order influence functions for bilinear forms.

Generative models improve commodity hedging using deep learning.

We compare two recently proposed methods that combine ideas from conformal inference and quantile regression to produce locally adaptive and marginally valid prediction intervals under sample exchangeability (Romano et al., 2019; Kivaranovic et al., 2019). First, we prove that these two approaches are asymptotically ef…

Recent policy optimization approaches have achieved substantial empirical success by constructing surrogate optimization objectives. The Approximate Policy Iteration objective (Schulman et al., 2015a; Kakade and Langford, 2002) has become a standard optimization target for reinforcement learning problems. Using this ob…

New methods improve inference after prediction without strong model assumptions.

In this article, we study the convergence of Mirror Descent (MD) and Optimistic Mirror Descent (OMD) for saddle point problems satisfying the notion of coherence as proposed in Mertikopoulos et al. We prove convergence of OMD with exact gradients for coherent saddle point problems, and show that monotone convergence on…

New model selects robustly in adversarial reinforcement learning with unknown corruption.

Meta-learning is a tool that allows us to build sample-efficient learning systems. Here we show that, once meta-trained, LSTM Meta-Learners aren't just faster learners than their sample-inefficient deep learning (DL) and reinforcement learning (RL) brethren, but that they actually pursue fundamentally different learnin…

Piecewise normalizing flows improve multi-modal distribution modeling.

We improve adversarial robustness calibration analysis for broader hypothesis sets.

New algorithms reduce matching market regret to log(T) with improved stability.

The paper analyzes and improves a deep learning optimization technique using matrix gradient orthogonality.

Study proves NN matching is equivalent to Riesz regression for debiased machine learning.

The backpropagation (BP) algorithm is often thought to be biologically implausible in the brain. One of the main reasons is that BP requires symmetric weight matrices in the feedforward and feedback pathways. To address this "weight transport problem" (Grossberg, 1987), two more biologically plausible algorithms, propo…

This comment reexamines Simard et al.'s work in [D. Simard, L. Nadeau, H. Kroger, Phys. Lett. A 336 (2005) 8-15]. We found that Simard et al. calculated mistakenly the local connectivity lengths Dlocal of networks. The right results of Dlocal are presented and the supervised learning performance of feedforward neural n…

Matrix factorization (MF) is a versatile learning method that has found wide applications in various data-driven disciplines. Still, many MF algorithms do not adequately scale with the size of available datasets and/or lack interpretability. To improve the computational efficiency of the method, an online (streaming) M…

Using deep neural networks that are either invariant or equivariant to permutations in order to learn functions on unordered sets has become prevalent. The most popular, basic models are DeepSets [Zaheer et al. 2017] and PointNet [Qi et al. 2017]. While known to be universal for approximating invariant functions, DeepS…

Although gradient descent (GD) almost always escapes saddle points asymptotically [Lee et al., 2016], this paper shows that even with fairly natural random initialization schemes and non-pathological functions, GD can be significantly slowed down by saddle points, taking exponential time to escape. On the other hand, g…

The paper reviews methods for determining the number of communities in network data.

Paper presents an efficient algorithm for linear MDP with low switching cost.

Deep latent variable models have become a popular model choice due to the scalable learning algorithms introduced by (Kingma & Welling, 2013; Rezende et al., 2014). These approaches maximize a variational lower bound on the intractable log likelihood of the observed data. Burda et al. (2015) introduced a multi-sample v…

Exploration and adaptation to new tasks in a transfer learning setup is a central challenge in reinforcement learning. In this work, we build on the idea of modeling a distribution over policies in a Bayesian deep reinforcement learning setup to propose a transfer strategy. Recent works have shown to induce diversity i…

This paper reports the performances of shallow word-level convolutional neural networks (CNN), our earlier work (2015), on the eight datasets with relatively large training data that were used for testing the very deep character-level CNN in Conneau et al. (2016). Our findings are as follows. The shallow word-level CNN…