Training a classifier with noisy labels typically requires the learner to specify the distribution of label noise, which is often unknown in practice. Although there have been some recent attempts to relax that requirement, we show that the Bayes decision rule is unidentified in most classification problems with noisy labels. This suggests it is generally not possible to bypass/relax the requirement. In the special cases in which the Bayes decision rule is identified, we develop a simple algorithm to learn the Bayes decision rule, that does not require knowledge of the noise distribution. In this paper, we consider classification with noisy labels.

The remarkable performance of overparameterized deep neural networks (DNNs) must arise from an interplay between network architecture, training algorithms, and structure in the data. To disentangle these three components, we apply a Bayesian picture, based on the functions expressed by a DNN, to supervised learning. The prior over functions is determined by the network, and is varied by exploiting a transition between ordered and chaotic regimes. For Boolean function classification, we approximate the likelihood using the error spectrum of functions on data. When combined with the prior, this accurately predicts the posterior, measured for DNNs trained with stochastic gradient descent. This analysis reveals that structured data, combined with an intrinsic Occam's razor-like inductive bias towards (Kolmogorov) simple functions that is strong enough to counteract the exponential growth of the number of functions with complexity, is a key to the success of DNNs.

The decision tree ensembles use a single data feature at each node for splitting the data. However, splitting in this manner may fail to capture the geometric properties of the data. Thus, oblique decision trees generate the oblique hyperplane for splitting the data at each non-leaf node. Oblique decision trees capture the geometric properties of the data and hence, show better generalization. The performance of the oblique decision trees depends on the way oblique hyperplanes are generate and the data used for the generation of those hyperplanes. Recently, multiple classifiers have been used in a heterogeneous random forest (RaF) classifier, however, it fails to generate the trees of proper depth. Moreover, double RaF studies highlighted that larger trees can be generated via bootstrapping the data at each non-leaf node and splitting the original data instead of the bootstrapped data recently. The study of heterogeneous RaF lacks the generation of larger trees while as the double RaF based model fails to take over the geometric characteristics of the data. To address these shortcomings, we propose heterogeneous oblique double RaF. The proposed model employs several linear classifiers at each non-leaf node on the bootstrapped data and splits the original data based on the optimal linear classifier. The optimal hyperplane corresponds to the models based on the optimized impurity criterion. The experimental analysis indicates that the performance of the introduced heterogeneous double random forest is comparatively better than the baseline models. To demonstrate the effectiveness of the proposed heterogeneous double random forest, we used it for the diagnosis of Schizophrenia disease. The proposed model predicted the disease more accurately compared to the baseline models.

Recently, there has been an arms race of pose forecasting methods aimed at solving the spatio-temporal task of predicting a sequence of future 3D poses of a person given a sequence of past observed ones. However, the lack of unified benchmarks and limited uncertainty analysis have hindered progress in the field. To address this, we first develop an open-source library for human pose forecasting, featuring multiple models, datasets, and standardized evaluation metrics, with the aim of promoting research and moving toward a unified and fair evaluation. Second, we devise two types of uncertainty in the problem to increase performance and convey better trust: 1) we propose a method for modeling Figure 1: We propose to model two kinds of uncertainty: aleatoric uncertainty by using uncertainty priors to inject 1) aleatoric uncertainty, learned by our model to capture knowledge about the behavior of uncertainty. This focuses the temporal evolution of uncertainty, which becomes more the capacity of the model in the direction of more meaningful prominent over time, as depicted by the lighter colors and supervision while reducing the number of learned parameters thicker bones for the right person; 2) epistemic uncertainty and improving stability; 2) we introduce a novel to detect out-of-distribution forecast poses coming from unseen approach for quantifying the epistemic uncertainty of any scenarios in training, such as for the left person.

This technical report studies the problem of ranking from pairwise comparisons in the classical Bradley-Terry-Luce (BTL) model, with a focus on score estimation. For general graphs, we show that, with sufficiently many samples, maximum likelihood estimation (MLE) achieves an entrywise estimation error matching the Cram\'er-Rao lower bound, which can be stated in terms of effective resistances; the key to our analysis is a connection between statistical estimation and iterative optimization by preconditioned gradient descent. We are also particularly interested in graphs with locality, where only nearby items can be connected by edges; our analysis identifies conditions under which locality does not hurt, i.e. comparing the scores between a pair of items that are far apart in the graph is nearly as easy as comparing a pair of nearby items. We further explore divide-and-conquer algorithms that can provably achieve similar guarantees even in the regime with the sparsest samples, while enjoying certain computational advantages. Numerical results validate our theory and confirm the efficacy of the proposed algorithms.

Biochemical reaction networks are an amalgamation of reactions where each reaction represents the interaction of different species. Generally, these networks exhibit a multi-scale behavior caused by the high variability in reaction rates and abundances of species. The so-called jump-diffusion approximation is a valuable tool in the modeling of such systems. The approximation is constructed by partitioning the reaction network into a fast and slow subgroup of fast and slow reactions, respectively. This enables the modeling of the dynamics using a Langevin equation for the fast group, while a Markov jump process model is kept for the dynamics of the slow group. Most often biochemical processes are poorly characterized in terms of parameters and population states. As a result of this, methods for estimating hidden quantities are of significant interest. In this paper, we develop a tractable Bayesian inference algorithm based on Markov chain Monte Carlo. The presented blocked Gibbs particle smoothing algorithm utilizes a sequential Monte Carlo method to estimate the latent states and performs distinct Gibbs steps for the parameters of a biochemical reaction network, by exploiting a jump-diffusion approximation model. The presented blocked Gibbs sampler is based on the two distinct steps of state inference and parameter inference. We estimate states via a continuous-time forward-filtering backward-smoothing procedure in the state inference step. By utilizing bootstrap particle filtering within a backward-smoothing procedure, we sample a smoothing trajectory. For estimating the hidden parameters, we utilize a separate Markov chain Monte Carlo sampler within the Gibbs sampler that uses the path-wise continuous-time representation of the reaction counters. Finally, the algorithm is numerically evaluated for a partially observed multi-scale birth-death process example.

In a randomized exam, each student is asked a small number of random questions from a large question bank. The predominant grading rule is simple averaging, i.e., calculating grades by averaging scores on the questions each student is asked, which is fair ex-ante, over the randomized questions, but not fair ex-post, on the realized questions. The fair grading problem is to estimate the average grade of each student on the full question bank. The maximum-likelihood estimator for the Bradley-Terry-Luce model on the bipartite student-question graph is shown to be consistent with high probability when the number of questions asked to each student is at least the cubed-logarithm of the number of students. In an empirical study on exam data and in simulations, our algorithm based on the maximum-likelihood estimator significantly outperforms simple averaging in prediction accuracy and ex-post fairness even with a small class and exam size.

Learning image classification and image generation using the same set of network parameters is a challenging problem. Recent advanced approaches perform well in one task often exhibit poor performance in the other. This work introduces an energy-based classifier and generator, namely EGC, which can achieve superior performance in both tasks using a single neural network. Unlike a conventional classifier that outputs a label given an image (i.e., a conditional distribution $p(y|\mathbf{x})$), the forward pass in EGC is a classifier that outputs a joint distribution $p(\mathbf{x},y)$, enabling an image generator in its backward pass by marginalizing out the label $y$. This is done by estimating the energy and classification probability given a noisy image in the forward pass, while denoising it using the score function estimated in the backward pass. EGC achieves competitive generation results compared with state-of-the-art approaches on ImageNet-1k, CelebA-HQ and LSUN Church, while achieving superior classification accuracy and robustness against adversarial attacks on CIFAR-10. This work represents the first successful attempt to simultaneously excel in both tasks using a single set of network parameters. We believe that EGC bridges the gap between discriminative and generative learning.

We study the design of sample-efficient algorithms for reinforcement learning in the presence of rich, high-dimensional observations, formalized via the Block MDP problem. Existing algorithms suffer from either 1) computational intractability, 2) strong statistical assumptions that are not necessarily satisfied in practice, or 3) suboptimal sample complexity. We address these issues by providing the first computationally efficient algorithm that attains rate-optimal sample complexity with respect to the desired accuracy level, with minimal statistical assumptions. Our algorithm, MusIK, combines systematic exploration with representation learning based on multi-step inverse kinematics, a learning objective in which the aim is to predict the learner's own action from the current observation and observations in the (potentially distant) future. MusIK is simple and flexible, and can efficiently take advantage of general-purpose function approximation. Our analysis leverages several new techniques tailored to non-optimistic exploration algorithms, which we anticipate will find broader use.

We conduct the first comprehensive meta-analysis of deterministic solar forecasting based on skill score, screening 1,447 papers from Google Scholar and reviewing the full texts of 320 papers for data extraction. A database of 4,687 points was built and analyzed with multivariate adaptive regression spline modelling, partial dependence plots, and linear regression. The marginal impacts on skill score of ten factors were quantified. The analysis shows the non-linearity and complex interaction between variables in the database. Forecast horizon has a central impact and dominates other factors' impacts. Therefore, the analysis of solar forecasts should be done separately for each horizon. Climate zone variables have statistically significant correlation with skill score. Regarding inputs, historical data and spatial temporal information are highly helpful. For intra-day, sky and satellite images show the most importance. For day-ahead, numerical weather predictions and locally measured meteorological data are very efficient. All forecast models were compared. Ensemble-hybrid models achieve the most accurate forecasts for all horizons. Hybrid models show superiority for intra-hour while image-based methods are the most efficient for intra-day forecasts. More training data can enhance skill score. However, over-fitting is observed when there is too much training data (longer than 2000 days). There has been a substantial improvement in solar forecast accuracy, especially in recent years. More improvement is observed for intra-hour and intra-day than day-ahead forecasts. By controlling for the key differences between forecasts, including location variables, our findings can be applied globally.