Zifan Li

Qi Lin, Zifan Li, John Lafferty et al.

Much of what we remember is not due to intentional selection, but simply a by-product of perceiving. This raises a foundational question about the architecture of the mind: How does perception interface with and influence memory? Here, inspired by a classic proposal relating perceptual processing to memory durability, the level-of-processing theory, we present a sparse coding model for compressing feature embeddings of images, and show that the reconstruction residuals from this model predict how well images are encoded into memory. In an open memorability dataset of scene images, we show that reconstruction error not only explains memory accuracy but also response latencies during retrieval, subsuming, in the latter case, all of the variance explained by powerful vision-only models. We also confirm a prediction of this account with 'model-driven psychophysics'. This work establishes reconstruction error as a novel signal interfacing perception and memory, possibly through adaptive modulation of perceptual processing.

Zifan Li, Ambuj Tewari

Recent work on follow the perturbed leader (FTPL) algorithms for the adversarial multi-armed bandit problem has highlighted the role of the hazard rate of the distribution generating the perturbations. Assuming that the hazard rate is bounded, it is possible to provide regret analyses for a variety of FTPL algorithms for the multi-armed bandit problem. This paper pushes the inquiry into regret bounds for FTPL algorithms beyond the bounded hazard rate condition. There are good reasons to do so: natural distributions such as the uniform and Gaussian violate the condition. We give regret bounds for both bounded support and unbounded support distributions without assuming the hazard rate condition. We also disprove a conjecture that the Gaussian distribution cannot lead to a low-regret algorithm. In fact, it turns out that it leads to near optimal regret, up to logarithmic factors. A key ingredient in our approach is the introduction of a new notion called the generalized hazard rate.

Zifan Li, Ambuj Tewari

Fictitious play is a simple and widely studied adaptive heuristic for playing repeated games. It is well known that fictitious play fails to be Hannan consistent. Several variants of fictitious play including regret matching, generalized regret matching and smooth fictitious play, are known to be Hannan consistent. In this note, we consider sampled fictitious play: at each round, the player samples past times and plays the best response to previous moves of other players at the sampled time points. We show that sampled fictitious play, using Bernoulli sampling, is Hannan consistent. Unlike several existing Hannan consistency proofs that rely on concentration of measure results, ours instead uses anti-concentration results from Littlewood-Offord theory.

Kam Chung Wong, Zifan Li, Ambuj Tewari

Many theoretical results on estimation of high dimensional time series require specifying an underlying data generating model (DGM). Instead, along the footsteps of~\cite{wong2017lasso}, this paper relies only on (strict) stationarity and $ β$-mixing condition to establish consistency of lasso when data comes from a $β$-mixing process with marginals having subgaussian tails. Because of the general assumptions, the data can come from DGMs different than standard time series models such as VAR or ARCH. When the true DGM is not VAR, the lasso estimates correspond to those of the best linear predictors using the past observations. We establish non-asymptotic inequalities for estimation and prediction errors of the lasso estimates. Together with~\cite{wong2017lasso}, we provide lasso guarantees that cover full spectrum of the parameters in specifications of $ β$-mixing subgaussian time series. Applications of these results potentially extend to non-Gaussian, non-Markovian and non-linear times series models as the examples we provide demonstrate. In order to prove our results, we derive a novel Hanson-Wright type concentration inequality for $β$-mixing subgaussian random vectors that may be of independent interest.