Gibbs sampling is a Markov Chain Monte Carlo sampling technique that iteratively samples variables from their conditional distributions. There are two common scan orders for the variables: random scan and systematic scan. Due to the benefits of locality in hardware, systematic scan is commonly used, even though most statistical guarantees are only for random scan. While it has been conjectured that the mixing times of random scan and systematic scan do not differ by more than a logarithmic factor, we show by counterexample that this is not the case, and we prove that that the mixing times do not differ by more than a polynomial factor under mild conditions. To prove these relative bounds, we introduce a method of augmenting the state space to study systematic scan using conductance.

In this work, we propose an infinite restricted Boltzmann machine (RBM), whose maximum likelihood estimation (MLE) corresponds to a constrained convex optimization. We consider the Frank-Wolfe algorithm to solve the program, which provides a sparse solution that can be interpreted as inserting a hidden unit at each iteration, so that the optimization process takes the form of a sequence of finite models of increasing complexity. As a side benefit, this can be used to easily and efficiently identify an appropriate number of hidden units during the optimization. The resulting model can also be used as an initialization for typical state-of-the-art RBM training algorithms such as contrastive divergence, leading to models with consistently higher test likelihood than random initialization.

In topic modeling, many algorithms that guarantee identifiability of the topics have been developed under the premise that there exist anchor words - i.e., words that only appear (with positive probability) in one topic. Follow-up work has resorted to three or higher-order statistics of the data corpus to relax the anchor word assumption. Reliable estimates of higher-order statistics are hard to obtain, however, and the identification of topics under those models hinges on uncorrelatedness of the topics, which can be unrealistic. This paper revisits topic modeling based on second-order moments, and proposes an anchor-free topic mining framework. The proposed approach guarantees the identification of the topics under a much milder condition compared to the anchor-word assumption, thereby exhibiting much better robustness in practice. The associated algorithm only involves one eigendecomposition and a few small linear programs. This makes it easy to implement and scale up to very large problem instances. Experiments using the TDT2 and Reuters-21578 corpus demonstrate that the proposed anchor-free approach exhibits very favorable performance (measured using coherence, similarity count, and clustering accuracy metrics) compared to the prior art.

We study the problem of completing a binary matrix in an online learning setting. On each trial we predict a matrix entry and then receive the true entry. We propose a Matrix Exponentiated Gradient algorithm [1] to solve this problem. We provide a mistake bound for the algorithm, which scales with the margin complexity [2, 3] of the underlying matrix. The bound suggests an interpretation where each row of the matrix is a prediction task over a finite set of objects, the columns. Using this we show that the algorithm makes a number of mistakes which is comparable up to a logarithmic factor to the number of mistakes made by the Kernel Perceptron with an optimal kernel in hindsight. We discuss applications of the algorithm to predicting as well as the best biclustering and to the problem of predicting the labeling of a graph without knowing the graph in advance.

It's already predicted the future, told terrible jokes, and demonstrated a range of realistic facial expressions including blinking and smiling. Now, British humanoid robot, Ameca, has been showing off its range of celebrity impressions – and they're eerily realistic. In a new video, the sophisticated machine – developed by Cornwall-based firm Engineered Arts – speaks in the style of Morgan Freeman, Elon Musk, and Donald Trump. Ameca is fitted with microphones, binocular eye mounted cameras, a chest camera and facial recognition software to interact with people. The robot has been described as the'world's most advanced' humanoid by Engineered Arts, and a'platform for human-robot interaction'. 'The aim here is to build the best expressive capabilities,' Engineered Arts says.

As datasets capturing human choices grow in richness and scale--particularly in online domains--there is an increasing need for choice models that escape traditional choice-theoretic axioms such as regularity, stochastic transitivity, and Luce's choice axiom. In this work we introduce the Pairwise Choice Markov Chain (PCMC) model of discrete choice, an inferentially tractable model that does not assume any of the above axioms while still satisfying the foundational axiom of uniform expansion, a considerably weaker assumption than Luce's choice axiom. We show that the PCMC model significantly outperforms both the Multinomial Logit (MNL) model and a mixed MNL (MMNL) model in prediction tasks on both synthetic and empirical datasets known to exhibit violations of Luce's axiom. Our analysis also synthesizes several recent observations connecting the Multinomial Logit model and Markov chains; the PCMC model retains the Multinomial Logit model as a special case.

Arkady Volozh, the billionaire cofounder of Russia's biggest internet company, was removed from the EU sanctions list today, clearing the way for his return to the world of international tech. On Tuesday a spokesperson for the European Council confirmed to WIRED that the Yandex cofounder was among three people whose sanctions were lifted this week. Volozh, 60, was initially included on the EU sanctions list in June 2023, following Russia's full-scale invasion of Ukraine in February 2022. "Volozh is a leading businessperson involved in economic sectors providing a substantial source of revenue to the Government of the Russian Federation," the bloc said last year to justify its decision. "As founder and CEO of Yandex, he is supporting, materially or financially, the Government of the Russian Federation."

Earlier this year, sexually explicit images of Taylor Swift were shared repeatedly X. The pictures were almost certainly created with generative-AI tools, demonstrating the ease with which the technology can be put to nefarious ends. This case mirrors many other apparently similar examples, including fake images depicting the arrest of former President Donald Trump, AI-generated images of Black voters who support Trump, and fabricated images of Dr. Anthony Fauci. There is a tendency for media coverage to focus on the source of this imagery, because generative AI is a novel technology that many people are still trying to wrap their head around. But that fact obscures the reason the images are relevant: They spread on social-media networks.

In October last year Francesa Mani came home from school in the suburbs of New Jersey with devastating news for her mother, Dorota. Earlier in the day the 14-year-old had been called into the vice-principal's office and notified that she and a group of girls at Westfield High had been the victims of targeted abuse by a fellow student. Faked nude images of her and others had been circulating around school. They had been generated by artificial intelligence. Dorota had been tangentially aware of the power of this relatively new technology, but the ease with which the images were generated took her aback.

We consider the problem of learning the underlying graph of an unknown Ising model on p spins from a collection of i.i.d.