We present the discovery of 816 high amplitude infrared variable stars ($Delta K_{rm s} >$ 1 mag) in 119 deg$^2$ of the Galactic midplane covered by the Vista Variables in the Via Lactea (VVV) survey. Almost all are new discoveries and about 50$%$ are YSOs. This provides further evidence that YSOs are the commonest high amplitude infrared variable stars in the Galactic plane. In the 2010-2014 time series of likely YSOs we find that the amplitude of variability increases towards younger evolutionary classes (class I and flat-spectrum sources) except on short timescales ($<$25 days) where this trend is reversed. Dividing the likely YSOs by light curve morphology, we find 106 with eruptive light curves, 45 dippers, 39 faders, 24 eclipsing binaries, 65 long-term periodic variables (P$>$100 days) and 162 short-term variables. Eruptive YSOs and faders tend to have the highest amplitudes and eruptive systems have the reddest SEDs. Follow up spectroscopy in a companion paper verifies high accretion rates in the eruptive systems. Variable extinction is disfavoured by the 2 epochs of colour data. These discoveries increase the number of eruptive variable YSOs by a factor of at least 5, most being at earlier stages of evolution than the known FUor and EXor types. We find that eruptive variability is at least an order of magnitude more common in class I YSOs than class II YSOs. Typical outburst durations are 1 to 4 years, between those of EXors and FUors. They occur in 3 to 6% of class I YSOs over a 4 year time span.
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