Our model extends the nested Chinese restaurant processes to discover tree-structured topic hierarchies and uses both per-topic hierarchical and per-word lexical regression parameters to model response variables.

Many modern systems, such as financial, transportation, and telecommunications systems, are time-sensitive in the sense that they demand low-latency predictions for real-time decision-making. Such systems often have to contend with continuous unbounded data streams as well as concept drift, which are challenging requirements that traditional regression techniques are unable to cater to. There exists a need to create novel data stream regression methods that can handle these scenarios. We present a database-inspired datastream regression model that (a) uses inspiration from R*-trees to create granules from incoming datastreams such that relevant information is retained, (b) iteratively forgets granules whose information is deemed to be outdated, thus maintaining a list of only recent, relevant granules, and (c) uses the recent data and granules to provide low-latency predictions. The R*-tree-inspired approach also makes the algorithm amenable to integration with database systems. Our experiments demonstrate that the ability of this method to discard data produces a significant order-of-magnitude improvement in latency and training time when evaluated against the most accurate state-of-the-art algorithms, while the R*-tree-inspired granulation technique provides competitively accurate predictions

Predictions in the form of probability distributions are crucial for decision-making. Quantile regression enables this within spatial interpolation settings for merging remote sensing and gauge precipitation data. However, ensemble learning of quantile regression algorithms remains unexplored in this context. Here, we address this gap by introducing nine quantile-based ensemble learners and applying them to large precipitation datasets. We employed a novel feature engineering strategy, reducing predictors to distance-weighted satellite precipitation at relevant locations, combined with location elevation. Our ensemble learners include six stacking and three simple methods (mean, median, best combiner), combining six individual algorithms: quantile regression (QR), quantile regression forests (QRF), generalized random forests (GRF), gradient boosting machines (GBM), light gradient boosting machines (LightGBM), and quantile regression neural networks (QRNN). These algorithms serve as both base learners and combiners within different stacking methods. We evaluated performance against QR using quantile scoring functions in a large dataset comprising 15 years of monthly gauge-measured and satellite precipitation in contiguous US (CONUS). Stacking with QR and QRNN yielded the best results across quantile levels of interest (0.025, 0.050, 0.075, 0.100, 0.200, 0.300, 0.400, 0.500, 0.600, 0.700, 0.800, 0.900, 0.925, 0.950, 0.975), surpassing the reference method by 3.91% to 8.95%. This demonstrates the potential of stacking to improve probabilistic predictions in spatial interpolation and beyond.

We establish theoretical results concerning local optima of regularized M-estimators, where both loss and penalty functions are allowed to be nonconvex. Our results show that as long as the loss satisfies restricted strong convexity and the penalty satisfies suitable regularity conditions, any local optimum of the composite objective lies within statistical precision of the true parameter vector. Our theory covers a broad class of nonconvex objective functions, including corrected versions of the Lasso for errors-in-variables linear models and regression in generalized linear models using nonconvex regularizers such as SCAD and MCP.

Differential privacy is a cryptographically motivated definition of privacy which has gained considerable attention in the algorithms, machine-learning and datamining communities. While there has been an explosion of work on differentially private machine learning algorithms, a major barrier to achieving end-to-end differential privacy in practical machine learning applications is the lack of an effective procedure for differentially private parameter tuning, or, determining the parameter value, such as a bin size in a histogram, or a regularization parameter, that is suitable for a particular application. In this paper, we introduce a generic validation procedure for differentially private machine learning algorithms that apply when a certain stability condition holds on the training algorithm and the validation performance metric. The training data size and the privacy budget used for training in our procedure is independent of the number of parameter values searched over. We apply our generic procedure to two fundamental tasks in statistics and machine-learning - training a regularized linear classifier and building a histogram density estimator that result in end-toend differentially private solutions for these problems.

A successful approach to structured learning is to write the learning objective as a joint function of linear parameters and inference messages, and iterate between updates to each. This paper observes that if the inference problem is "smoothed" through the addition of entropy terms, for fixed messages, the learning objective reduces to a traditional (non-structured) logistic regression problem with respect to parameters. In these logistic regression problems, each training example has a bias term determined by the current set of messages. Based on this insight, the structured energy function can be extended from linear factors to any function class where an "oracle" exists to minimize a logistic loss.

We establish lower bounds on minimax risks for distributed statistical estimation under a communication budget. Such lower bounds reveal the minimum amount of communication required by any procedure to achieve the centralized minimax-optimal rates for statistical estimation. We study two classes of protocols: one in which machines send messages independently, and a second allowing for interactive communication. We establish lower bounds for several problems, including various types of location models, as well as for parameter estimation in regression models.

Simply showing that there is information about actions, actors (and their conjunction) in any part of the brain does not mean they have tackled a "(three-fold) challenge". One would find (presumably) very similar response properties in any part of the mirror neuron system. Furthermore, if one analysed retinal cells, one would also find this information. Perhaps you could highlight the fact that you have found information or invariance properties at the level of the single neuron - that could not be found at low levels in the visual hierarchy - to make your point more clearly?

Fitting high-dimensional statistical models often requires the use of non-linear parameter estimation procedures. As a consequence, it is generally impossible to obtain an exact characterization of the probability distribution of the parameter estimates. This in turn implies that it is extremely challenging to quantify the uncertainty associated with a certain parameter estimate. Concretely, no commonly accepted procedure exists for computing classical measures of uncertainty and statistical significance as confidence intervals or p-values. We consider here a broad class of regression problems, and propose an efficient algorithm for constructing confidence intervals and p-values.

We present a new approach to sample from generic binary distributions, based on an exact Hamiltonian Monte Carlo algorithm applied to a piecewise continuous augmentation of the binary distribution of interest. An extension of this idea to distributions over mixtures of binary and possibly-truncated Gaussian or exponential variables allows us to sample from posteriors of linear and probit regression models with spike-and-slab priors and truncated parameters. We illustrate the advantages of these algorithms in several examples in which they outperform the Metropolis or Gibbs samplers.