Bayesian inference in state-space models is challenging due to high-dimensional state trajectories. A viable approach is particle Markov chain Monte Carlo, combining MCMC and sequential Monte Carlo to form "exact approximations" to otherwise intractable MCMC methods. The performance of the approximation is limited to that of the exact method. We focus on particle Gibbs and particle Gibbs with ancestor sampling, improving their performance beyond that of the underlying Gibbs sampler (which they approximate) by marginalizing out one or more parameters. This is possible when the parameter prior is conjugate to the complete data likelihood. Marginalization yields a non-Markovian model for inference, but we show that, in contrast to the general case, this method still scales linearly in time. While marginalization can be cumbersome to implement, recent advances in probabilistic programming have enabled its automation. We demonstrate how the marginalized methods are viable as efficient inference backends in probabilistic programming, and demonstrate with examples in ecology and epidemiology.

Clustering is one of the most fundamental and wide-spread techniques in exploratory data analysis. Yet, the basic approach to clustering has not really changed: a practitioner hand-picks a task-specific clustering loss to optimize and fit the given data to reveal the underlying cluster structure. Some types of losses---such as k-means, or its non-linear version: kernelized k-means (centroid based), and DBSCAN (density based)---are popular choices due to their good empirical performance on a range of applications. Although every so often the clustering output using these standard losses fails to reveal the underlying structure, and the practitioner has to custom-design their own variation. In this work we take an intrinsically different approach to clustering: rather than fitting a dataset to a specific clustering loss, we train a recurrent model that learns how to cluster. The model uses as training pairs examples of datasets (as input) and its corresponding cluster identities (as output). By providing multiple types of training datasets as inputs, our model has the ability to generalize well on unseen datasets (new clustering tasks). Our experiments reveal that by training on simple synthetically generated datasets or on existing real datasets, we can achieve better clustering performance on unseen real-world datasets when compared with standard benchmark clustering techniques. Our meta clustering model works well even for small datasets where the usual deep learning models tend to perform worse.

The potential for learned models to amplify existing societal biases has been broadly recognized. Fairness-aware classifier constraints, which apply equality metrics of performance across subgroups defined on sensitive attributes such as race and gender, seek to rectify inequity but can yield non-uniform degradation in performance for skewed datasets. In certain domains, imbalanced degradation of performance can yield another form of unintentional bias. In the spirit of constructing fairness-aware algorithms as societal imperative, we explore an alternative: Pareto-Efficient Fairness (PEF). Theoretically, we prove that PEF identifies the operating point on the Pareto curve of subgroup performances closest to the fairness hyperplane, maximizing multiple subgroup accuracy. Empirically we demonstrate that PEF outperforms by achieving Pareto levels in accuracy for all subgroups compared to strict fairness constraints in several UCI datasets.

In the problem of learning mixtures of linear regressions, the goal is to learn a collection of signal vectors from a sequence of (possibly noisy) linear measurements, where each measurement is evaluated on an unknown signal drawn uniformly from this collection. This setting is quite expressive and has been studied both in terms of practical applications and for the sake of establishing theoretical guarantees. In this paper, we consider the case where the signal vectors are sparse; this generalizes the popular compressed sensing paradigm. We improve upon the state-of-the-art results as follows: In the noisy case, we resolve an open question of Yin et al. (IEEE Transactions on Information Theory, 2019) by showing how to handle collections of more than two vectors and present the first robust reconstruction algorithm, i.e., if the signals are not perfectly sparse, we still learn a good sparse approximation of the signals. In the noiseless case, as well as in the noisy case, we show how to circumvent the need for a restrictive assumption required in the previous work. Our techniques are quite different from those in the previous work: for the noiseless case, we rely on a property of sparse polynomials and for the noisy case, we provide new connections to learning Gaussian mixtures and use ideas from the theory of error-correcting codes.

The perception of facial beauty is a complex phenomenon depending on many, detailed and global facial features influencing each other. In the machine learning community this problem is typically tackled as a problem of supervised inference. However, it has been conjectured that this approach does not capture the complexity of the phenomenon. A recent original experiment (Ib\'a\~nez-Berganza et al., Scientific Reports 9, 8364, 2019) allowed different human subjects to navigate the face-space and "sculpt" their preferred modification of a reference facial portrait. Here we present an unsupervised inference study of the set of sculpted facial vectors in that experiment. We first infer minimal, interpretable, and faithful probabilistic models (through Maximum Entropy and artificial neural networks) of the preferred facial variations, that capture the origin of the observed inter-subject diversity in the sculpted faces. The application of such generative models to the supervised classification of the gender of the sculpting subjects, reveals an astonishingly high prediction accuracy. This result suggests that much relevant information regarding the subjects may influence (and be elicited from) her/his facial preference criteria, in agreement with the multiple motive theory of attractiveness proposed in previous works.

We introduce a "learning-based" algorithm for the low-rank decomposition problem: given an $n \times d$ matrix $A$, and a parameter $k$, compute a rank-$k$ matrix $A'$ that minimizes the approximation loss $\|A-A'\|_F$. The algorithm uses a training set of input matrices in order to optimize its performance. Specifically, some of the most efficient approximate algorithms for computing low-rank approximations proceed by computing a projection $SA$, where $S$ is a sparse random $m \times n$ "sketching matrix", and then performing the singular value decomposition of $SA$. We show how to replace the random matrix $S$ with a "learned" matrix of the same sparsity to reduce the error. Our experiments show that, for multiple types of data sets, a learned sketch matrix can substantially reduce the approximation loss compared to a random matrix $S$, sometimes by one order of magnitude. We also study mixed matrices where only some of the rows are trained and the remaining ones are random, and show that matrices still offer improved performance while retaining worst-case guarantees. Finally, to understand the theoretical aspects of our approach, we study the special case of $m=1$. In particular, we give an approximation algorithm for minimizing the empirical loss, with approximation factor depending on the stable rank of matrices in the training set. We also show generalization bounds for the sketch matrix learning problem.

The use of momentum in stochastic gradient methods has become a widespread practice in machine learning. Different variants of momentum, including heavy-ball momentum, Nesterov's accelerated gradient (NAG), and quasi-hyperbolic momentum (QHM), have demonstrated success on various tasks. Despite these empirical successes, there is a lack of clear understanding of how the momentum parameters affect convergence and various performance measures of different algorithms. In this paper, we use the general formulation of QHM to give a unified analysis of several popular algorithms, covering their asymptotic convergence conditions, stability regions, and properties of their stationary distributions. In addition, by combining the results on convergence rates and stationary distributions, we obtain sometimes counter-intuitive practical guidelines for setting the learning rate and momentum parameters.

Machine learning has proved to be very successful for making predictions in travel behavior modeling. However, most machine-learning models have complex model structures and offer little or no explanation as to how they arrive at these predictions. Interpretations about travel behavior models are essential for decision makers to understand travelers' preferences and plan policy interventions accordingly. Therefore, this paper proposes to apply and extend the model distillation approach, a model-agnostic machine-learning interpretation method, to explain how a black-box travel mode choice model makes predictions for the entire population and subpopulations of interest. Model distillation aims at compressing knowledge from a complex model (teacher) into an understandable and interpretable model (student). In particular, the paper integrates model distillation with market segmentation to generate more insights by accounting for heterogeneity. Furthermore, the paper provides a comprehensive comparison of student models with the benchmark model (decision tree) and the teacher model (gradient boosting trees) to quantify the fidelity and accuracy of the students' interpretations.

We present an algorithm for extraction of a probabilistic deterministic finite automaton (PDFA) from a given black-box language model, such as a recurrent neural network (RNN). The algorithm is a variant of the exact-learning algorithm L*, adapted to a probabilistic setting with noise. The key insight is the use of conditional probabilities for observations, and the introduction of a local tolerance when comparing them. When applied to RNNs, our algorithm often achieves better word error rate (WER) and normalised distributed cumulative gain (NDCG) than that achieved by spectral extraction of weighted finite automata (WFA) from the same networks. PDFAs are substantially more expressive than n-grams, and are guaranteed to be stochastic and deterministic - unlike spectrally extracted WFAs.

We analyze the practices of reservoir computing in the framework of statistical learning theory. In particular, we derive finite sample upper bounds for the generalization error committed by specific families of reservoir computing systems when processing discrete-time inputs under various hypotheses on their dependence structure. Non-asymptotic bounds are explicitly written down in terms of the multivariate Rademacher complexities of the reservoir systems and the weak dependence structure of the signals that are being handled. This allows, in particular, to determine the minimal number of observations needed in order to guarantee a prescribed estimation accuracy with high probability for a given reservoir family. At the same time, the asymptotic behavior of the devised bounds guarantees the consistency of the empirical risk minimization procedure for various hypothesis classes of reservoir functionals.