Multi-View Active Learning in the Non-Realizable Case

The sample complexity of active learning under the realizability assumption has been well-studied. The realizability assumption, however, rarely holds in practice. In this paper, we theoretically characterize the sample complexity of active learning in the non-realizable case under multi-view setting. We prove that, with unbounded Tsybakov noise, the sample complexity of multi-view active learning can be $\widetilde{O}(\log\frac{1}{\epsilon})$, contrasting to single-view setting where the polynomial improvement is the best possible achievement. We also prove that in general multi-view setting the sample complexity of active learning with unbounded Tsybakov noise is $\widetilde{O}(\frac{1}{\epsilon})$, where the order of $1/\epsilon$ is independent of the parameter in Tsybakov noise, contrasting to previous polynomial bounds where the order of $1/\epsilon$ is related to the parameter in Tsybakov noise.Comment: 22 pages, 1 figur

Order flow dynamics around extreme price changes on an emerging stock market

We study the dynamics of order flows around large intraday price changes using ultra-high-frequency data from the Shenzhen Stock Exchange. We find a significant reversal of price for both intraday price decreases and increases with a permanent price impact. The volatility, the volume of different types of orders, the bid-ask spread, and the volume imbalance increase before the extreme events and decay slowly as a power law, which forms a well-established peak. The volume of buy market orders increases faster and the corresponding peak appears earlier than for sell market orders around positive events, while the volume peak of sell market orders leads buy market orders in the magnitude and time around negative events. When orders are divided into four groups according to their aggressiveness, we find that the behaviors of order volume and order number are similar, except for buy limit orders and canceled orders that the peak of order number postpones two minutes later after the peak of order volume, implying that investors placing large orders are more informed and play a central role in large price fluctuations. We also study the relative rates of different types of orders and find differences in the dynamics of relative rates between buy orders and sell orders and between individual investors and institutional investors. There is evidence showing that institutions behave very differently from individuals and that they have more aggressive strategies. Combing these findings, we conclude that institutional investors are more informed and play a more influential role in driving large price fluctuations.Comment: 22 page

Preferred numbers and the distribution of trade sizes and trading volumes in the Chinese stock market

The distribution of trade sizes and trading volumes are investigated based on the limit order book data of 22 liquid Chinese stocks listed on the Shenzhen Stock Exchange in the whole year 2003. We observe that the size distribution of trades for individual stocks exhibits jumps, which is caused by the number preference of traders when placing orders. We analyze the applicability of the "$q$-Gamma" function for fitting the distribution by the Cram\'{e}r-von Mises criterion. The empirical PDFs of trading volumes at different timescales $\Delta{t}$ ranging from 1 min to 240 min can be well modeled. The applicability of the $q$-Gamma functions for multiple trades is restricted to the transaction numbers $\Delta{n}\leqslant8$. We find that all the PDFs have power-law tails for large volumes. Using careful estimation of the average tail exponents $\alpha$ of the distribution of trade sizes and trading volumes, we get $\alpha>2$, well outside the L{\'e}vy regime.Comment: 7 pages, 5 figures and 4 table

Modeling of residual spheres for subduction zone earthquakes: 1. Apparent slab penetration signatures in the NW Pacific caused by deep diffuse mantle anomalies

We have computed focal residual spheres for 145 subduction zone earthquakes along the northwest edge of the Pacific using regional and global mantle velocity models from tomographic inversions. The mantle models explain much of the observed residual sphere data and, to a certain extent, suggest the location of mantle velocity heterogeneities which are responsible for various residual sphere patterns. For most deep events considered, the fast slablike residual sphere anomalies are caused by diffuse heterogeneities, mainly of deep lower mantle and receiver mantle origin rather than by an extension of the slab. The region immediately below the deepest earthquakes, depths of 650–1500 km, has an effect usually smaller than or comparable to the effect of other regions of the mantle. Without a proper account of the teleseismic effect, attributing the long-wavelength anomalies of the residual sphere to near-source slab effects alone, or even primarily, is not valid. The fast bands in many observed residual spheres agree with seismicity trends. Once the deep mantle and receiver mantle effects are removed, these may give the approximate orientation, but not the depth extent, of near-source fast velocities. For most deep earthquakes under Japan the predominant fast band is subhorizontal rather than near vertical. This type feature would be overlooked in conventional residual sphere studies using only steeply diving rays and cosine weighting of the data