Related papers: Comparison of objective functions for estimating l…
In recent years, functional linear models have attracted growing attention in statistics and machine learning, with the aim of recovering the slope function or its functional predictor. This paper considers online regularized learning…
A fundamental problem in neuroscience is to characterize the dynamics of spiking from the neurons in a circuit that is involved in learning about a stimulus or a contingency. A key limitation of current methods to analyze neural spiking…
In binary classification tasks, accurate representation of probabilistic predictions is essential for various real-world applications such as predicting payment defaults or assessing medical risks. The model must then be well-calibrated to…
In system identification, estimating parameters of a model using limited observations results in poor identifiability. To cope with this issue, we propose a new method to simultaneously select and estimate sensitive parameters as key model…
Kernel methods provide a flexible and theoretically grounded approach to nonlinear and nonparametric learning. While memory and run-time requirements hinder their applicability to large datasets, many low-rank kernel approximations, such as…
This paper proposes a paradigm shift linking machine unlearning directly to the structure of the data distributions rather than a mere update of the neural network parameters. We show that inferring these distributions with precision…
Rational and neural network based approximations are efficient tools in modern approximation. These approaches are able to produce accurate approximations to nonsmooth and non-Lipschitz functions, including multivariate domain functions. In…
A spiking neuron ``computes'' by transforming a complex dynamical input into a train of action potentials, or spikes. The computation performed by the neuron can be formulated as dimensional reduction, or feature detection, followed by a…
When pre-processing observational data via matching, we seek to approximate each unit with maximally similar peers that had an alternative treatment status--essentially replicating a randomized block design. However, as one considers a…
Use of nonlinear feature maps via kernel approximation has led to success in many online learning tasks. As a popular kernel approximation method, Nystr\"{o}m approximation, has been well investigated, and various landmark points selection…
Extracting a small subset of crucial rationales from the full input is a key problem in explainability research. The most widely used fundamental criterion for rationale extraction is the maximum mutual information (MMI) criterion. In this…
Deep neural networks (DNN) trained in a supervised way suffer from two known problems. First, the minima of the objective function used in learning correspond to data points (also known as rubbish examples or fooling images) that lack…
We propose a new framework for Imitation Learning (IL) via density estimation of the expert's occupancy measure followed by Maximum Occupancy Entropy Reinforcement Learning (RL) using the density as a reward. Our approach maximizes a…
We investigate the problem of estimating the causal effect of a treatment on individual subjects from observational data, this is a central problem in various application domains, including healthcare, social sciences, and online…
Nonlinear Noisy Leaky Integrate and Fire (NNLIF) models for neurons networks can be written as Fokker-Planck-Kolmogorov equations on the probability density of neurons, the main parameters in the model being the connectivity of the network…
We consider in this paper the optimal approximations of convex univariate functions with feed-forward Relu neural networks. We are interested in the following question: what is the minimal approximation error given the number of…
Stimulus from the environment that guides behavior and informs decisions is encoded in the firing rates of neural populations. Each neuron in the populations, however, does not spike independently: spike events are correlated from cell to…
Distributionally robust offline reinforcement learning (RL), which seeks robust policy training against environment perturbation by modeling dynamics uncertainty, calls for function approximations when facing large state-action spaces.…
A general method for deriving maximally informative sigmoidal tuning curves for neural systems with small normalized variability is presented. The optimal tuning curve is a nonlinear function of the cumulative distribution function of the…
This paper investigates the score-based diffusion models for density estimation when the target density admits a factorizable low-dimensional nonparametric structure. To be specific, we show that when the log density admits a $d^*$-way…