We address the problem of comparing the risks of two given predictive models - for instance, a baseline model and a challenger - as confidently as possible on a fixed labeling budget. This problem occurs whenever models cannot be compared on held-out training data, possibly because the training data are unavailable or do not reflect the desired test distribution. In this case, new test instances have to be drawn and labeled at a cost. We devise an active comparison method that selects instances according to an instrumental sampling distribution. We derive the sampling distribution that maximizes the power of a statistical test applied to the observed empirical risks, and thereby minimizes the likelihood of choosing the inferior model. Empirically, we investigate model selection problems on several classification and regression tasks and study the accuracy of the resulting p-values.

In conventional causal discovery, structural equation models (SEM) are directly applied to the observed variables, meaning that the causal effect can be represented as a function of the direct causes themselves. However, in many real world problems, there are significant dependencies in the variances or energies, which indicates that causality may possibly take place at the level of variances or energies. In this paper, we propose a probabilistic causal scale-mixture model with spatiotemporal variance dependencies to represent a specific type of generating mechanism of the observations. In particular, the causal mechanism including contemporaneous and temporal causal relations in variances or energies is represented by a Structural Vector AutoRegressive model (SVAR). We prove the identifiability of this model under the non-Gaussian assumption on the innovation processes. We also propose algorithms to estimate the involved parameters and discover the contemporaneous causal structure. Experiments on synthesis and real world data are conducted to show the applicability of the proposed model and algorithms.

Memristive devices have recently been proposed as efficient implementations of plastic synapses in neuromorphic systems. The plasticity in these memristive devices, i.e. their resistance change, is defined by the applied waveforms. This behavior resembles biological synapses, whose plasticity is also triggered by mechanisms that are determined by local waveforms. However, learning in memristive devices has so far been approached mostly on a pragmatic technological level. The focus seems to be on finding any waveform that achieves spike-timing-dependent plasticity (STDP), without regard to the biological veracity of said waveforms or to further important forms of plasticity. Bridging this gap, we make use of a plasticity model driven by neuron waveforms that explains a large number of experimental observations and adapt it to the characteristics of the recently introduced BiFeO$_3$ memristive material. Based on this approach, we show STDP for the first time for this material, with learning window replication superior to previous memristor-based STDP implementations. We also demonstrate in measurements that it is possible to overlay short and long term plasticity at a memristive device in the form of the well-known triplet plasticity. To the best of our knowledge, this is the first implementations of triplet plasticity on any physical memristive device.

Statistical learning and sequential prediction are two different but related formalisms to study the quality of predictions. Mapping out their relations and transferring ideas is an active area of investigation. We provide another piece of the puzzle by showing that an important concept in sequential prediction, the mixability of a loss, has a natural counterpart in the statistical setting, which we call stochastic mixability. Just as ordinary mixability characterizes fast rates for the worst-case regret in sequential prediction, stochastic mixability characterizes fast rates in statistical learning. We show that, in the special case of log-loss, stochastic mixability reduces to a well-known (but usually unnamed) martingale condition, which is used in existing convergence theorems for minimum description length and Bayesian inference. In the case of 0/1-loss, it reduces to the margin condition of Mammen and Tsybakov, and in the case that the model under consideration contains all possible predictors, it is equivalent to ordinary mixability.

We study the problem of learning local metrics for nearest neighbor classification. Most previous works on local metric learning learn a number of local unrelated metrics. While this ''independence'' approach delivers an increased flexibility its downside is the considerable risk of overfitting. We present a new parametric local metric learning method in which we learn a smooth metric matrix function over the data manifold. Using an approximation error bound of the metric matrix function we learn local metrics as linear combinations of basis metrics defined on anchor points over different regions of the instance space. We constrain the metric matrix function by imposing on the linear combinations manifold regularization which makes the learned metric matrix function vary smoothly along the geodesics of the data manifold. Our metric learning method has excellent performance both in terms of predictive power and scalability. We experimented with several large-scale classification problems, tens of thousands of instances, and compared it with several state of the art metric learning methods, both global and local, as well as to SVM with automatic kernel selection, all of which it outperforms in a significant manner.

This paper discusses the problem of calibrating posterior class probabilities from partially labelled data. Each instance is assumed to be labelled as belonging to one of several candidate categories, at most one of them being true. We generalize the concept of proper loss to this scenario, establish a necessary and sufficient condition for a loss function to be proper, and we show a direct procedure to construct a proper loss for partial labels from a conventional proper loss. The problem can be characterized by the mixing probability matrix relating the true class of the data and the observed labels. An interesting result is that the full knowledge of this matrix is not required, and losses can be constructed that are proper in a subset of the probability simplex.

Partially-observable Markov decision processes (POMDPs) provide a powerful model for real-world sequential decision-making problems. In recent years, point- based value iteration methods have proven to be extremely effective techniques for finding (approximately) optimal dynamic programming solutions to POMDPs when an initial set of belief states is known. However, no point-based work has provided exact point-based backups for both continuous state and observation spaces, which we tackle in this paper. Our key insight is that while there may be an infinite number of possible observations, there are only a finite number of observation partitionings that are relevant for optimal decision-making when a finite, fixed set of reachable belief states is known. To this end, we make two important contributions: (1) we show how previous exact symbolic dynamic pro- gramming solutions for continuous state MDPs can be generalized to continu- ous state POMDPs with discrete observations, and (2) we show how this solution can be further extended via recently developed symbolic methods to continuous state and observations to derive the minimal relevant observation partitioning for potentially correlated, multivariate observation spaces. We demonstrate proof-of- concept results on uni- and multi-variate state and observation steam plant control.

While compressive sensing (CS) has been one of the most vibrant and active research fields in the past few years, most development only applies to linear models. This limits its application and excludes many areas where CS ideas could make a difference. This paper presents a novel extension of CS to the phase retrieval problem, where intensity measurements of a linear system are used to recover a complex sparse signal. We propose a novel solution using a lifting technique -- CPRL, which relaxes the NP-hard problem to a nonsmooth semidefinite program. Our analysis shows that CPRL inherits many desirable properties from CS, such as guarantees for exact recovery. We further provide scalable numerical solvers to accelerate its implementation. The source code of our algorithms will be provided to the public.

Topic modeling is a widely used approach to analyzing large text collections. A small number of multilingual topic models have recently been explored to discover latent topics among parallel or comparable documents, such as in Wikipedia. Other topic models that were originally proposed for structured data are also applicable to multilingual documents. Correspondence Latent Dirichlet Allocation (CorrLDA) is one such model; however, it requires a pivot language to be specified in advance. We propose a new topic model, Symmetric Correspondence LDA (SymCorrLDA), that incorporates a hidden variable to control a pivot language, in an extension of CorrLDA. We experimented with two multilingual comparable datasets extracted from Wikipedia and demonstrate that SymCorrLDA is more effective than some other existing multilingual topic models.

The Lovasz $\theta$ function of a graph, is a fundamental tool in combinatorial optimization and approximation algorithms. Computing $\theta$ involves solving a SDP and is extremely expensive even for moderately sized graphs. In this paper we establish that the Lovasz $\theta$ function is equivalent to a kernel learning problem related to one class SVM. This interesting connection opens up many opportunities bridging graph theoretic algorithms and machine learning. We show that there exist graphs, which we call $SVM-\theta$ graphs, on which the Lovasz $\theta$ function can be approximated well by a one-class SVM. This leads to a novel use of SVM techniques to solve algorithmic problems in large graphs e.g. identifying a planted clique of size $\Theta({\sqrt{n}})$ in a random graph $G(n,\frac{1}{2})$. A classic approach for this problem involves computing the $\theta$ function, however it is not scalable due to SDP computation. We show that the random graph with a planted clique is an example of $SVM-\theta$ graph, and as a consequence a SVM based approach easily identifies the clique in large graphs and is competitive with the state-of-the-art. Further, we introduce the notion of a ''common orthogonal labeling'' which extends the notion of a ''orthogonal labelling of a single graph (used in defining the $\theta$ function) to multiple graphs. The problem of finding the optimal common orthogonal labelling is cast as a Multiple Kernel Learning problem and is used to identify a large common dense region in multiple graphs. The proposed algorithm achieves an order of magnitude scalability compared to the state of the art.