Changes in real-world dynamic processes are often described in terms of differences in energies $\textbf{E}(\underline{\alpha})$ of a set of spectral-bands $\underline{\alpha}$. Given continuous spectra of two classes $A$ and $B$, or in general, two stochastic processes $S^{(A)}(f)$ and $S^{(B)}(f)$, $f \in \mathbb{R}^+$, we address the ubiquitous problem of identifying a subset of intervals of $f$ called spectral-bands $\underline{\alpha} \subset \mathbb{R}^+$ such that the energies $\textbf{E}(\underline{\alpha})$ of these bands can optimally discriminate between the two classes. We introduce EGO-MDA, an unsupervised method to identify optimal spectral-bands $\underline{\alpha}^*$ for given samples of spectra from two classes. EGO-MDA employs a statistical approach that iteratively minimizes an adjusted multinomial log-likelihood (deviance) criterion $\mathcal{D}(\underline{\alpha},\mathcal{M})$. Here, Mixture Discriminant Analysis (MDA) aims to derive MLE of two GMM distribution parameters, i.e., $\mathcal{M}^* = \underset{\mathcal{M}}{\rm argmin}~\mathcal{D}(\underline{\alpha}, \mathcal{M})$ and identify a classifier that optimally discriminates between two classes for a given spectral representation. The Efficient Global Optimization (EGO) finds the spectral-bands $\underline{\alpha}^* = \underset{\underline{\alpha}}{\rm argmin}~\mathcal{D}(\underline{\alpha},\mathcal{M})$ for given GMM parameters $\mathcal{M}$. For pathological cases of low separation between mixtures and model misspecification, we discuss the effect of the sample size and the number of iterations on the estimates of parameters $\mathcal{M}$ and therefore the classifier performance. A case study on a synthetic data set is provided. In an engineering application of optimal spectral-banding for anomaly tracking, EGO-MDA achieved at least 70% improvement in the median deviance relative to other methods tested.

Advances in reinforcement learning have led to its successful application in complex tasks with continuous state and action spaces. Despite these advances in practice, most theoretical work pertains to finite state and action spaces. We propose building a theoretical understanding of continuous state and action spaces by employing a geometric lens. Central to our work is the idea that the transition dynamics induce a low dimensional manifold of reachable states embedded in the high-dimensional nominal state space. We prove that, under certain conditions, the dimensionality of this manifold is at most the dimensionality of the action space plus one. This is the first result of its kind, linking the geometry of the state space to the dimensionality of the action space. We empirically corroborate this upper bound for four MuJoCo environments. We further demonstrate the applicability of our result by learning a policy in this low dimensional representation. To do so we introduce an algorithm that learns a mapping to a low dimensional representation, as a narrow hidden layer of a deep neural network, in tandem with the policy using DDPG. Our experiments show that a policy learnt this way perform on par or better for four MuJoCo control suite tasks.

Deep neural networks can approximate functions on different types of data, from images to graphs, with varied underlying structure. This underlying structure can be viewed as the geometry of the data manifold. By extending recent advances in the theoretical understanding of neural networks, we study how a randomly initialized neural network with piece-wise linear activation splits the data manifold into regions where the neural network behaves as a linear function. We derive bounds on the density of boundary of linear regions and the distance to these boundaries on the data manifold. This leads to insights into the expressivity of randomly initialized deep neural networks on non-Euclidean data sets. We empirically corroborate our theoretical results using a toy supervised learning problem. Our experiments demonstrate that number of linear regions varies across manifolds and the results hold with changing neural network architectures. We further demonstrate how the complexity of linear regions is different on the low dimensional manifold of images as compared to the Euclidean space, using the MetFaces dataset.

In recent years multi-label, multi-class video action recognition has gained significant popularity. While reasoning over temporally connected atomic actions is mundane for intelligent species, standard artificial neural networks (ANN) still struggle to classify them. In the real world, atomic actions often temporally connect to form more complex composite actions. The challenge lies in recognising composite action of varying durations while other distinct composite or atomic actions occur in the background. Drawing upon the success of relational networks, we propose methods that learn to reason over the semantic concept of objects and actions. We empirically show how ANNs benefit from pretraining, relational inductive biases and unordered set-based latent representations. In this paper we propose deep set conditioned I3D (SCI3D), a two stream relational network that employs latent representation of state and visual representation for reasoning over events and actions. They learn to reason about temporally connected actions in order to identify all of them in the video. The proposed method achieves an improvement of around 1.49% mAP in atomic action recognition and 17.57% mAP in composite action recognition, over a I3D-NL baseline, on the CATER dataset.

Maximum Inner Product Search (MIPS) is a popular problem in the machine learning literature due to its applicability in a wide array of applications, such as recommender systems. In high-dimensional settings, however, MIPS queries can become computationally expensive as most existing solutions do not scale well with data dimensionality. In this work, we present a state-of-the-art algorithm for the MIPS problem in high dimensions, dubbed BanditMIPS. BanditMIPS is a randomized algorithm that borrows techniques from multi-armed bandits to reduce the MIPS problem to a best-arm identification problem. BanditMIPS reduces the complexity of state-of-the-art algorithms from $O(\sqrt{d})$ to $O(\text{log}d)$, where $d$ is the dimension of the problem data vectors. On high-dimensional real-world datasets, BanditMIPS runs approximately 12 times faster than existing approaches and returns the same solution. BanditMIPS requires no preprocessing of the data and includes a hyperparameter that practitioners may use to trade off accuracy and runtime. We also propose a variant of our algorithm, named BanditMIPS-$\alpha$, which employs non-uniform sampling across the data dimensions to provide further speedups.

Motivated by mitigating potentially harmful impacts of technologies, the AI community has formulated and accepted mathematical definitions for certain pillars of accountability: e.g. privacy, fairness, and model transparency. Yet, we argue this is fundamentally misguided because these definitions are imperfect, siloed constructions of the human values they hope to proxy, while giving the guise that those values are sufficiently embedded in our technologies. Under popularized methods, tensions arise when practitioners attempt to achieve each pillar of fairness, privacy, and transparency in isolation or simultaneously. In this position paper, we push for redirection. We argue that the AI community needs to consider all the consequences of choosing certain formulations of these pillars -- not just the technical incompatibilities, but also the effects within the context of deployment. We point towards sociotechnical research for frameworks for the latter, but push for broader efforts into implementing these in practice.

Random forests are some of the most widely used machine learning models today, especially in domains that necessitate interpretability. We present an algorithm that accelerates the training of random forests and other popular tree-based learning methods. At the core of our algorithm is a novel node-splitting subroutine, dubbed MABSplit, used to efficiently find split points when constructing decision trees. Our algorithm borrows techniques from the multi-armed bandit literature to judiciously determine how to allocate samples and computational power across candidate split points. We provide theoretical guarantees that MABSplit improves the sample complexity of each node split from linear to logarithmic in the number of data points. In some settings, MABSplit leads to 100x faster training (an 99% reduction in training time) without any decrease in generalization performance. We demonstrate similar speedups when MABSplit is used across a variety of forest-based variants, such as Extremely Random Forests and Random Patches. We also show our algorithm can be used in both classification and regression tasks. Finally, we show that MABSplit outperforms existing methods in generalization performance and feature importance calculations under a fixed computational budget. All of our experimental results are reproducible via a one-line script at https://github.com/ThrunGroup/FastForest.

Developing and least developed countries face the dire challenge of ensuring that each child in their country receives required doses of vaccination, adequate nutrition and proper medication. International agencies such as UNICEF, WHO and WFP, among other organizations, strive to find innovative solutions to determine which child has received the benefits and which have not. Biometric recognition systems have been sought out to help solve this problem. To that end, this report establishes a baseline accuracy of a commercial contactless palmprint recognition system that may be deployed for recognizing children in the age group of one to five years old. On a database of contactless palmprint images of one thousand unique palms from 500 children, we establish SOTA authentication accuracy of 90.85% @ FAR of 0.01%, rank-1 identification accuracy of 99.0% (closed set), and FPIR=0.01 @ FNIR=0.3 for open-set identification using PalmMobile SDK from Armatura.

Concept bottleneck models (CBMs) (Koh et al. 2020) are interpretable neural networks that first predict labels for human-interpretable concepts relevant to the prediction task, and then predict the final label based on the concept label predictions.We extend CBMs to interactive prediction settings where the model can query a human collaborator for the label to some concepts. We develop an interaction policy that, at prediction time, chooses which concepts to request a label for so as to maximally improve the final prediction. We demonstrate thata simple policy combining concept prediction uncertainty and influence of the concept on the final prediction achieves strong performance and outperforms a static approach proposed in Koh et al. (2020) as well as active feature acquisition methods proposed in the literature. We show that the interactiveCBM can achieve accuracy gains of 5-10% with only 5 interactions over competitive baselines on the Caltech-UCSDBirds, CheXpert and OAI datasets.

Reliable uncertainty quantification in deep neural networks is very crucial in safety-critical applications such as automated driving for trustworthy and informed decision-making. Assessing the quality of uncertainty estimates is challenging as ground truth for uncertainty estimates is not available. Ideally, in a well-calibrated model, uncertainty estimates should perfectly correlate with model error. We propose a novel error aligned uncertainty optimization method and introduce a trainable loss function to guide the models to yield good quality uncertainty estimates aligning with the model error. Our approach targets continuous structured prediction and regression tasks, and is evaluated on multiple datasets including a large-scale vehicle motion prediction task involving real-world distributional shifts. We demonstrate that our method improves average displacement error by 1.69% and 4.69%, and the uncertainty correlation with model error by 17.22% and 19.13% as quantified by Pearson correlation coefficient on two state-of-the-art baselines.