We consider a sequential learning problem with Gaussian payoffs and side information: after selecting an action $i$, the learner receives information about the payoff of every action $j$ in the form of Gaussian observations whose mean is the same as the mean payoff, but the variance depends on the pair $(i,j)$ (and may be infinite). The setup allows a more refined information transfer from one action to another than previous partial monitoring setups, including the recently introduced graph-structured feedback case. For the first time in the literature, we provide non-asymptotic problem-dependent lower bounds on the regret of any algorithm, which recover existing asymptotic problem-dependent lower bounds and finite-time minimax lower bounds available in the literature. We also provide algorithms that achieve the problem-dependent lower bound (up to some universal constant factor) or the minimax lower bounds (up to logarithmic factors).

We study the problem of reducing test-time acquisition costs in classification systems. Our goal is to learn decision rules that adaptively select sensors for each example as necessary to make a confident prediction. We model our system as a directed acyclic graph (DAG) where internal nodes correspond to sensor subsets and decision functions at each node choose whether to acquire a new sensor or classify using the available measurements. This problem can be naturally posed as an empirical risk minimization over training data. Rather than jointly optimizing such a highly coupled and non-convex problem over all decision nodes, we propose an efficient algorithm motivated by dynamic programming. We learn node policies in the DAG by reducing the global objective to a series of cost sensitive learning problems. Our approach is computationally efficient and has proven guarantees of convergence to the optimal system for a fixed architecture. In addition, we present an extension to map other budgeted learning problems with large number of sensors to our DAG architecture and demonstrate empirical performance exceeding state-of-the-art algorithms for data composed of both few and many sensors.

This paper concerns a method of selecting a subset of features for a sequential logit model. Tanaka and Nakagawa (2014) proposed a mixed integer quadratic optimization formulation for solving the problem based on a quadratic approximation of the logistic loss function. However, since there is a significant gap between the logistic loss function and its quadratic approximation, their formulation may fail to find a good subset of features. To overcome this drawback, we apply a piecewise-linear approximation to the logistic loss function. Accordingly, we frame the feature subset selection problem of minimizing an information criterion as a mixed integer linear optimization problem. The computational results demonstrate that our piecewise-linear approximation approach found a better subset of features than the quadratic approximation approach.

In this position paper, I argue that standardized tests for elementary science such as SAT or Regents tests are not very good benchmarks for measuring the progress of artificial intelligence systems in understanding basic science. The primary problem is that these tests are designed to test aspects of knowledge and ability that are challenging for people; the aspects that are challenging for AI systems are very different. In particular, standardized tests do not test knowledge that is obvious for people; none of this knowledge can be assumed in AI systems. Individual standardized tests also have specific features that are not necessarily appropriate for an AI benchmark. I analyze the Physics subject SAT in some detail and the New York State Regents Science test more briefly. I also argue that the apparent advantages offered by using standardized tests are mostly either minor or illusory. The one major real advantage is that the significance is easily explained to the public; but I argue that even this is a somewhat mixed blessing. I conclude by arguing that, first, more appropriate collections of exam style problems could be assembled, and second, that there are better kinds of benchmarks than exam-style problems. In an appendix I present a collection of sample exam-style problems that test kinds of knowledge missing from the standardized tests.

We study an equivalence of (i) deterministic pathwise statements appearing in the online learning literature (termed \emph{regret bounds}), (ii) high-probability tail bounds for the supremum of a collection of martingales (of a specific form arising from uniform laws of large numbers for martingales), and (iii) in-expectation bounds for the supremum. By virtue of the equivalence, we prove exponential tail bounds for norms of Banach space valued martingales via deterministic regret bounds for the online mirror descent algorithm with an adaptive step size. We extend these results beyond the linear structure of the Banach space: we define a notion of \emph{martingale type} for general classes of real-valued functions and show its equivalence (up to a logarithmic factor) to various sequential complexities of the class (in particular, the sequential Rademacher complexity and its offset version). For classes with the general martingale type 2, we exhibit a finer notion of variation that allows partial adaptation to the function indexing the martingale. Our proof technique rests on sequential symmetrization and on certifying the \emph{existence} of regret minimization strategies for certain online prediction problems.

In an earlier work we have used the Triangular Fuzzy Numbers (TFNs)as an assessment tool of student skills.This approach led to an approximate linguistic characterization of the students' overall performance, but it was not proved to be sufficient in all cases for comparing the performance of two different student groups, since tywo TFNs are not always comparable. In the present paper we complete the above fuzzy assessment approach by presenting a defuzzification method of TFNS based on the Center of Gravity (COG) technique, which enables the required comparison. In addition we extend our results by using the Trapezoidal Fuzzy Numbers (TpFNs) too, which are a generalization of the TFNs, for student assessment and we present suitable examples illustrating our new results in practice.

In this paper we introduce a novel online time series forecasting model we refer to as the pM-GP filter. We show that our model is equivalent to Gaussian process regression, with the advantage that both online forecasting and online learning of the hyper-parameters have a constant (rather than cubic) time complexity and a constant (rather than squared) memory requirement in the number of observations, without resorting to approximations. Moreover, the proposed model is expressive in that the family of covariance functions of the implied latent process, namely the spectral Matern kernels, have recently been proven to be capable of approximating arbitrarily well any translation-invariant covariance function. The benefit of our approach compared to competing models is demonstrated using experiments on several real-life datasets.

Top-performing machine learning systems, such as deep neural networks, large ensembles and complex probabilistic graphical models, can be expensive to store, slow to evaluate and hard to integrate into larger systems. Ideally, we would like to replace such cumbersome models with simpler models that perform equally well. In this thesis, we study knowledge distillation, the idea of extracting the knowledge contained in a complex model and injecting it into a more convenient model. We present a general framework for knowledge distillation, whereby a convenient model of our choosing learns how to mimic a complex model, by observing the latter's behaviour and being penalized whenever it fails to reproduce it. We develop our framework within the context of three distinct machine learning applications: (a) model compression, where we compress large discriminative models, such as ensembles of neural networks, into models of much smaller size; (b) compact predictive distributions for Bayesian inference, where we distil large bags of MCMC samples into compact predictive distributions in closed form; (c) intractable generative models, where we distil unnormalizable models such as RBMs into tractable models such as NADEs. We contribute to the state of the art with novel techniques and ideas. In model compression, we describe and implement derivative matching, which allows for better distillation when data is scarce. In compact predictive distributions, we introduce online distillation, which allows for significant savings in memory. Finally, in intractable generative models, we show how to use distilled models to robustly estimate intractable quantities of the original model, such as its intractable partition function.

We consider the problem of distributed multi-task learning, where each machine learns a separate, but related, task. Specifically, each machine learns a linear predictor in high-dimensional space,where all tasks share the same small support. We present a communication-efficient estimator based on the debiased lasso and show that it is comparable with the optimal centralized method.

Humans can learn the use of language through physical interaction with their environment and semiotic communication with other people. It is very important to obtain a computational understanding of how humans can form a symbol system and obtain semiotic skills through their autonomous mental development. Recently, many studies have been conducted on the construction of robotic systems and machine-learning methods that can learn the use of language through embodied multimodal interaction with their environment and other systems. Understanding human social interactions and developing a robot that can smoothly communicate with human users in the long term, requires an understanding of the dynamics of symbol systems and is crucially important. The embodied cognition and social interaction of participants gradually change a symbol system in a constructive manner. In this paper, we introduce a field of research called symbol emergence in robotics (SER). SER is a constructive approach towards an emergent symbol system. The emergent symbol system is socially self-organized through both semiotic communications and physical interactions with autonomous cognitive developmental agents, i.e., humans and developmental robots. Specifically, we describe some state-of-art research topics concerning SER, e.g., multimodal categorization, word discovery, and a double articulation analysis, that enable a robot to obtain words and their embodied meanings from raw sensory--motor information, including visual information, haptic information, auditory information, and acoustic speech signals, in a totally unsupervised manner. Finally, we suggest future directions of research in SER.