For data assumed to come from a finite mixture with an unknown number of components, it has become common to use Dirichlet process mixtures (DPMs) not only for density estimation, but also for inferences about the number of components. The typical approach is to use the posterior distribution on the number of clusters -- that is, the posterior on the number of components represented in the observed data. However, it turns out that this posterior is not consistent -- it does not concentrate at the true number of components. In this note, we give an elementary proof of this inconsistency in what is perhaps the simplest possible setting: a DPM with normal components of unit variance, applied to data from a "mixture" with one standard normal component. Further, we show that this example exhibits severe inconsistency: instead of going to 1, the posterior probability that there is one cluster converges (in probability) to 0.

It is well known that the optimal convergence rate for stochastic optimization of smooth functions is O(1/ T), which is same as stochastic optimization of Lipschitz continuous convex functions.

This paper proposes a hierarchical, supervised topic model that builds on ideas from hierarchical LDA using the nested CRP and from supervised LDA, which associates topics with regression coefficients. The proposed model further extends hierarchical LDA by allowing each sentence in a document to chose its own path through the topic tree, and sharing of paths for sentences within the same document is modelled through a document-level CRP where the customers are sentences and the dishes are paths through the topic hierarchy ("combos"). Another difference to supervised LDA is that each word is also associated with its own regression coefficient to model topic-independent effects. The authors empirically demonstrate the performance of the model on 3 data sets and show that the proposed model outperforms LDA linear regression as well as supervised LDA. The idea of modelling framing in the proposed way by associating regression coefficients with hierarchically arranged topics is interesting and appears novel.

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.

We propose an approximate inference algorithm for continuous time Gaussian Markov process models with both discrete and continuous time likelihoods. We show that the continuous time limit of the expectation propagation algorithm exists and results in a hybrid fixed point iteration consisting of (1) expectation propagation updates for discrete time terms and (2) variational updates for the continuous time term. We introduce postinference corrections methods that improve on the marginals of the approximation. This approach extends the classical Kalman-Bucy smoothing procedure to non-Gaussian observations, enabling continuous-time inference in a variety of models, including spiking neuronal models (state-space models with point process observations) and box likelihood models. Experimental results on real and simulated data demonstrate high distributional accuracy and significant computational savings compared to discrete-time approaches in a neural application.

Mixture models (MM) assume that instances are drawn from a mixture of K component distributions with unknown coefficients. Topic models (TM), on the other hand, assume that samples/documents have different mixing weights of the underlying topic distribution over words. This paper tries to close the gap between MM and TM. Their proposed model assumes that several samples are drawn from the same underlying K distributions, but similar to TM, has different mixing weights and assume that instances are treated as feature vectors similar to MM. This is a theory paper that provides two algorithms that can recover the underlying structure for this model.

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

In the context of visual perception, the optical signal from a scene is transferred into the electronic domain by detectors in the form of image data, which are then processed for the extraction of visual information. In noisy and weak-signal environments such as thermal imaging for night vision applications, however, the performance of neural computing tasks faces a significant bottleneck due to the inherent degradation of data quality upon noisy detection. Here, we propose a concept of optical signal processing before detection to address this issue. We demonstrate that spatially redistributing optical signals through a properly designed linear transformer can enhance the detection noise resilience of visual perception tasks, as benchmarked with the MNIST classification. Our idea is supported by a quantitative analysis detailing the relationship between signal concentration and noise robustness, as well as its practical implementation in an incoherent imaging system. This compute-first detection scheme can pave the way for advancing infrared machine vision technologies widely used for industrial and defense applications.

Benchmarking models via classical simulations is one of the main ways to judge ideas in quantum machine learning before noise-free hardware is available. However, the huge impact of the experimental design on the results, the small scales within reach today, as well as narratives influenced by the commercialisation of quantum technologies make it difficult to gain robust insights. To facilitate better decision-making we develop an open-source package based on the PennyLane software framework and use it to conduct a large-scale study that systematically tests 12 popular quantum machine learning models on 6 binary classification tasks used to create 160 individual datasets. We find that overall, out-of-the-box classical machine learning models outperform the quantum classifiers. Moreover, removing entanglement from a quantum model often results in as good or better performance, suggesting that "quantumness" may not be the crucial ingredient for the small learning tasks considered here. Our benchmarks also unlock investigations beyond simplistic leaderboard comparisons, and we identify five important questions for quantum model design that follow from our results.

Gradient Descent Ascent (GDA) methods for min-max optimization problems typically produce oscillatory behavior that can lead to instability, e.g., in bilinear settings. To address this problem, we introduce a dissipation term into the GDA updates to dampen these oscillations. The proposed Dissipative GDA (DGDA) method can be seen as performing standard GDA on a state-augmented and regularized saddle function that does not strictly introduce additional convexity/concavity. We theoretically show the linear convergence of DGDA in the bilinear and strongly convex-strongly concave settings and assess its performance by comparing DGDA with other methods such as GDA, Extra-Gradient (EG), and Optimistic GDA. Our findings demonstrate that DGDA surpasses these methods, achieving superior convergence rates. We support our claims with two numerical examples that showcase DGDA's effectiveness in solving saddle point problems.